Fill in the Blanks

• If a body changes its position with respect to its surroundings, the body is said to be in …………..

If a body changes its position with respect to its surroundings, the body is said to be in motion.

Motion is a relative concept.

• The distance can never be ………., while displacement can be.

The distance can never be negative, while displacement can be.

Distance is always positive while displacement can be positive or negative or zero.

• If a body moves such that it covers equal distances in equal intervals of time, whatsoever be small, then the object is said to have …………. motion.

If a body moves such that it covers equal distances in equal intervals of time, whatsoever be small, then the object is said to have uniform motion.

• When a particle moves in a straight line from point A to point B the distance covered is ………. the magnitude of the displacement.

When a particle moves in a straight line from point A to point B the distance covered is equal to the magnitude of the displacement.

• Distance travelled divided by elapsed time gives ………….

Distance travelled divided by elapsed time gives speed.

• The ratio of the total displacement of a body to the total time taken is …………

The ratio of the total displacement of a body to the total time taken is velocity.

The average velocity of an object moving on a circle of radius R in one complete rotation if it takes t second in completing one rotation is …………..

The average velocity of an object moving on a circle of radius R in one complete rotation if it takes t second in completing one rotation is zero.

In one complete rotation displacement of the object is zero

Velocity = Displacement/time = 0/t = 0

• An object moving uniformly on a circular track. Its velocity ………. with time.

An object moving uniformly on a circular track. Its velocity changes with time.

In uniform circular motion, the speed (magnitude of velocity) is constant, but the direction of velocity changes continuously. Hence body in circular motion moves with acceleration.

• If particle is moving along circular path such that in equal interval of time it describes the equal angle, then velocity vector …………

If particle is moving along circular path such that in equal interval of time it describes the equal angle, then velocity vector changes its direction continuously.

The particle describes the equal angle in equal interval of time. Hence particle is in uniform circular motion. In uniform circular motion, the speed (magnitude of velocity) is constant, but the direction of velocity changes continuously.

• The magnitude of average velocity ………… equal to the average speed.

The magnitude of average velocity may or may not be equal to the average speed.

• When a body has unequal displacement in equal intervals of time, it is said to be moving with …………..

When a body has unequal displacement in equal intervals of time, it is said to be moving with non-uniform velocity.

• The acceleration of freely falling object is approximately equal to ……..

The acceleration of freely falling object is approximately equal to 9.8 ms^-2.

• If a body starts from rest and moves with uniform acceleration, then its displacement is proportional to ………….

If a body starts from rest and moves with uniform acceleration, then its displacement is proportional to square of time.

s = ut + 1/2 at²

now u = 0

s = 1/2 at²

• A particle is just released to fall down from the top of a building. Its velocity at a particular position is directly proportional to …….

A particle is just released to fall down from the top of a building. Its velocity at a particular position is directly proportional to ………

A particle is just released to fall down from the top of a building. Its velocity at a particular position is directly proportional to time.

v = u + at

now u = 0

v = at

• All objects in free fall at a given place have the same

All objects in free fall at a given place have the same acceleration.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.

• …………… acceleration is called retardation or deceleration.

Negative acceleration is called retardation or deceleration.

• A car is moving northward. The driver of the car applies brakes, the direction of acceleration is …………..

A car is moving northward. The driver of the car applies brakes, the direction of acceleration is southward.

When brakes are applied, the acceleration is negative and acts in the opposite direction to tht of motion at the instant of braking.

• A body moving with constant speed has zero acceleration only when the particle is in …… dimensional motion.

A body moving with constant speed has zero acceleration only when the particle is in one dimensional motion.

• In velocity-time graph, velocity is taken on ……… axis.

In velocity-time graph, velocity is taken on x-axis

• Area under velocity-time graph gives …………..

Area under velocity-time graph gives the displacement.

• The velocity-time graph of a moving object is a straight line parallel to the time axis. It means the velocity of the object is ………..

The velocity-time graph of a moving object is a straight line parallel to the time axis. It means the velocity of the object is constant.

• The velocity-time graph of a body moving with uniform velocity is a straight line parallel to …………..

The velocity-time graph of a body moving with uniform velocity is a straight line parallel to time axis.

The post Motion in a Straight Line Fill in the Blanks Questions appeared first on The Fact Factor.

In last few articles, we have seen the concept of a motion in a straight line. From this article we shall apply the concept. In this article we shall study true and false type questions based on a motion in a straight line.

State whether the following statements are true or false. If false correct the statement.

• The travel of a train from one station to another is an example of translatory motion.

True

In translational motion every particle of the body has the same displacement.

• Motion of an ant along one of the edge of table is translatory motion.

True

In translational motion every particle of the body has the same displacement.

• The magnitude of displacement can be equal to or lesser than the distance travelled.

True

The shortest distance from the initial position to the final position of the body is called the magnitude of the displacement. Thus in case of body moving in a straight line in the same direction, the maximum displacement can be equal to the distance travelled. In all other case, it will be less than the distance travelled.

• Ddistance covered by a moving body is always greater than zero.

True.

• Displacement of a particle can be less than or greater than or equal to zero.

True

• Uniform speed is a vector quantity

False

Correction: Speed is a scalar quantity

Speed = distance / time, in this formula, both the dstance travelled and time are scalar quantities, hence speed is a scalar quantity.

• A particle moving with a uniform velocity must be along a straight line.

True.

Since velocity is a vector quantity it has both the magnitude and direction and if direction changes it is not uniform velocity. In case of circular motion there is a continuous change in direction leading to accelarated motion which results in non uniform velocity.

• A body can have a constant speed and still have varying velocity.

True. 

In a uniform circular motion, the speed of the body is constant but due to continuous change in direction, the velocity is varying. A body can not have its velocity constant, while its speed varies.

• The magnitude of average velocity is always equal to the average speed.

False.

Correction: The magnitude of average velocity ned not be equal to the average speed.

In a uniform circular motion, the speed of the body is constant but due to continuous change in direction, the velocity is varying. The magnitude of the average velocity of an object is equal to its average speed, only in one condition when an object is moving in a straight line.

• Average velocity can be calculated by taking the average of initial and final velocities for a given time interval irrespective of the type of acceleration.

True

• For a body moving along a circular path, the average velocity and average speed can never be equal.

True.

In a uniform circular motion, the speed of the body is constant but due to continuous change in direction, the velocity is varying. Thus in case of uniform ciercular motion, average speed is constant and equal to the magnitude of the instantaneous velocity of the body, but average velocity is zero.

• Average velocity can be zero, but average speed of a moving body can not be zero in any finite time interval.

True

uniform ciercular motion, average speed is constant and equal to the magnitude of the instantaneous velocity of the body, but average velocity is zero.

• If a body moves with constant velocity, its displacement depends on depends on square of time

False

Correction: If a body moves with constant velocity, its displacement depends on depends on time

v = ds/dt = k = constant

Integrating both sides with time t

s = kt

Thus displacement varies directly with time (t)

• A particle speed is constant, acceleration of the particle must be zero.

False

Correction: A particle speed is constant, acceleration of the particle need not be zero.

In a uniform circular motion, the speed of the body is constant but due to continuous change in direction, the velocity is varying. Thus particle possesses acceleration.

• When a particle moves with a constant speed in the same direction, neither the magnitude nor the direction of velocity changes and so acceleration is zero.

True

Since velocity is a vector quantity it has both the magnitude and direction. In this case both the speed and direction are the same. Hence the particle is moving with a constant velocity and has zero acceleration.

• A particle is known to be at rest at time t = 0. If its acceleration at t = 0 is zero.

False

Correction: A particle is known to be at rest at time t = 0. If its velocity at t = 0 is zero.

A body is said to be at rest if it does not change its position with respect to its immediate surroundings. Thus the velocity of the body decides its state of motion.

• An object covers distances in direct proportion to the square of the time elapsed. Its acceleration is increasing.

False

An object covers distances in direct proportion to the square of the time elapsed. Its acceleration is constant

s = kt² (given)

Differentiating both sides w.r.t. time t

velocity = v = ds/dt = 2kt

Differentiating both sides again w.r.t. time t

acceleration = a = dv/dt = 2k = constant

Thus in this case acceleration is constant. i.e. the object is moving with constant acceleration.

• A particle in one-dimensional motion with a positive value of acceleration must be speeding up.

False

A particle in one-dimensional motion with a positive value of acceleration may or may not be speeding up.

If the initial velocity of a body is negative then even in case of positive acceleration, the body speeds down. 

• There can be a motion in which speed is constant but velocity is variable.

True

In uniform circular motion, speed is constant but velocity is variable.

• A body moves with retardation when it is projected vertically upward.

True

Every body on the earth surface is acted upon by gravitational force acting in downward direction. When a body is projected vertically upward, due to the action of the gravitational force, its velocity goes on decreasing. Thus the body moves with retardation. at the highest point of its journey its velocity is zero.

• A body is projected vertically up. On reaching maximum height, its velocity becomes zero.

True

Every body on the earth surface is acted upon by gravitational force acting in downward direction. When a body is projected vertically upward, due to the action of the gravitational force, its velocity goes on decreasing. Thus the body moves with retardation. at the highest point of its journey its velocity is zero.

• A stone dropped from a height moves with constant velocity

False

Correction: A stone dropped from a height moves with constant acceleration.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.

• When two balls of different masses are thrown vertically upwards with the same initial speed, the heavier body rises to greater height then the lighter body.

False

Correction: When two balls of different masses are thrown vertically upwards with the same initial speed, both the bodies will rise to the same maximum height.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity. The height reached by the body epends on the initial speed by which they are thrown ipwards and the acceleration due to gravity at that place. Both the bodies will be acted upon by the same acceleration due to gravity and they are projected with same initial speed. hence both the bodies will rise to the same height.

• The distance travelled by a freely falling body in every successive second is the same.

False:

Correction: The distance travelled by a freely falling body in every successive second increases.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity. Thus freely falling body moves with acceleration due to gravity in downward direction i.e. in the direction of motion, hence its speed increases continuously and thus it covers more distance in every successice second.

• The area under the velocity-time diagram shows the displacement of the body

True

• Velocity-time graph cannot be used to find the instantaneous velocity

False

Correction: Velocity-time graph can be used to find the instantaneous velocity

• Velocity-time graph can be used to find displacement of the body.

True

The area under the velocity-time diagram shows the displacement of the body

• Equations of motion are applicable only when a body moves with uniform velocity.

False

Correction: Equations of motion are applicable only when a body moves with uniform acceleration.

• Direction of motion is decided by the displacement of a body.

False

Direction of motion is decided by the velocity of a body. Positive value of velocity indicates body is moving in the direction of the displacement while neghative value of velocity indicates the body is moving in the opposite direction to that of displacement.

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The post Motion in a Straight Line True and False Questions appeared first on The Fact Factor.

In the last article we have studied the concept of speed and velocity. Motion is an important part of our life. Our daily activities involve motion of different kinds. When we study motion, we come across another important concept namely acceleration. In this article, we shall study the the concept of uniform acceleration.

Notes
Very Short Answer Type Questions
Short Answer Type Questions
Concept Application

Velocity:

The rate of change of displacement of a body with respect to time is called the velocity of the body.

Velocity = Displacement / Time

Velocity is a vector quantity, its S.I. unit is m/s and c.g.s. unit is cm/s. Its dimensions are [L¹M⁰T^-1].

Uniform Velocity: 

When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform velocity. For uniform motion acceleration a = 0 and Displacement = velocity × time.

Example: The velocity of light in a particular medium is uniform velocity.  The velocity of sound in air at constant temperature is uniform velocity.

Non Uniform Velocity: 

When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have the nonuniform velocity or variable velocity.

A body can have non-uniform velocity in the following three cases.

• When the direction of the velocity of a body remains the same but its magnitude changes continuously then the body has variable velocity. e.g. a ball is thrown vertically upward.
• When the magnitude of the velocity of a body remains the same but the direction changes continuously then the body has variable velocity. e.g. uniform circular motion of a body.
• When both the magnitude and direction of the velocity of body change continuously, then the body has variable velocity. e.g. ball thrown by making the acute angle with the horizontal (projectile motion)

When a body has variable velocity, then it has acceleration.

Acceleration:

The rate of change of velocity with respect to time is called acceleration.

Acceleration is vector quantity its S.I. unit is m/s². Its dimensions are [L¹M⁰T^-2].

Acceleration = (v – u)/t

Where, u = Initial velocity

v = Final velocity

t = Time in which the change takes place

Acceleration can be positive, negative or zero. If the velocity is increasing then acceleration is positive. If the velocity is decreasing acceleration is negative. If the velocity is the constant acceleration is zero. Negative acceleration is also called deceleration or retardation.

If the velocity is increasing then the direction of acceleration is same as that of the velocity of the body. If the velocity is decreasing then the direction of acceleration is opposite to that of the velocity of the body.

It is to be noted that the velocity and not the acceleration of the body determines the direction of motion.

Uniform Acceleration:

When equal changes take place in the velocity of a body in equal interval of time, then the acceleration is called uniform acceleration. e.g. the motion under gravity.

Variable Acceleration:

When The change in the velocity of a body in equal interval of time is not constant, then the acceleration is called non-uniform acceleration. Example: the motion of a vehicle on crowded road.

Acceleration Due To Gravity:

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.

It is denoted by ‘g’. It varies from place to place. The average value of g at sea level is taken as 9.8 ms^-2 in S.I. system and 980 cms^-2 in c.g.s. system. When solving problems on the motion under gravity as per the convention the value of ‘g’ should be negative.

Relation Between Velocity and Acceleration:

• When both velocity and acceleration are positive, acceleration is in the direction of velocity and velocity increases.
• When velocity is positive and acceleration is negative, the acceleration is in the opposite direction of the velocity and velocity decreases.
• When velocity is negative and acceleration is positive, the acceleration is in opposite direction of velocity and velocity increases but body is moving in opposite direction.
• When both velocity and acceleration are negative, acceleration is in the direction of velocity and velocity decreases but body is moving in opposite direction.

Concepts:

Very Short Answer Type Questions

Q1. The average value of acceleration due to gravity at sea level is …… ms^-2

The average value of acceleration due to gravity at sea level is 9.8 ms^-2

Q2. Define acceleration.

The rate of change of velocity with respect to time is called acceleration

Q3. Give c.g.s., m.k.s. and S.I. units of acceleration.

Q4. Retardation is ……….. quantity

Retardation is a vector quantity

Q5. ……. acceleration is called retardation or deceleration.

Negative acceleration is called retardation or deceleration.

Q6. A freely falling body falls with …………..

A freely falling body falls with uniform acceleration, called acceleration due to gravity.

Q7. When is a body said to have zero acceleration?

If a body is at rest or moving with uniform velocity, then the body is said to have zero acceleration.

Q8. What is the acceleration of a body when its velocity remains constant?

In such case the acceleration of the body is zero.

Q9. What is acceleration due to gravity?

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.

Q10. Rate of decrease in the magnitude of velocity is called ……..

Rate of decrease in the magnitude of velocity is called retadation or deceleration.

Q11. Give one example of each type of following motions

Uniform acceleration: free fall of a body under influence of gravity

Variable acceleration: A motion of vehicle on crowded road

Q12. What is retardation?

Negative acceleration is called retardation or deceleration.

Q13. Is acceleration due to gravity constant everywhere?

Acceleration due to gravity is not constant everywhere. It depends on altitude, depth, shape of earth, and latitude of the place. It is maximum at the poles and minimum at the equator.

Short Answer Type Questions

Q1. Explain the term ‘acceleration due to gravity’.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.

It is denoted by ‘g’. It varies from place to place. The average value of g at sea level is taken as 9.8 ms^-2 in S.I. system and 980 cms^-2 in c.g.s. system. When solving problems on the motion under gravity as per the convention the value of ‘g’ should be negative.

Q2. Which of the following bodies does hit the ground first when realeased from the same height simultaneously: a body of mass 1 kg or a body of mass 10 kg.

When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity. The value of g does not depend on mass of the body. If the two bodies of different masses are dropped from the same height simultaneusly, both will reach ground simultaneously, if the effect of air (friction and buoyancy) is neglected.

Q3. Distinguish between acceleration and retardation.

Q4. Distinguish between uniform acceleration and variable acceleration.

Concept Application:

Q1. A train moving with a speed 90 kmph is brought to rest in 10 s. Find its retardation.

u = Initial velocity = 90 kmph = 90 x (5/18) = 25 ms^-1

v = Final velocity = 0

Time in which change is brought = 10 s

We have acceleration = a = (v – u)/t

a = (0 – 25)/10 = – 2.5 ms^-2

Negative sign indicates retardation.

Q2. A car initially at rest attains velocity of 20 ms^-1 with uniform acceleration in 2.5 s. What is its acceleration?

u = Initial velocity = 0

v = Final velocity = 20 ms^-1

Time in which change is brought = 2.5 s

We have acceleration = a = (v – u)/t

a = (20 – 0)/2.5 = 8 ms^-2

Q3. The velocity of an object increases at a constant rate 20 m s^-1 to 50 m s^-1 in 10s. Find the acceleration.

Given: Initial velocity = u = 20 m s^-1, Final velocity = v = 50 m s^-1, Time elapsed = t = 10 s.

To Find: Acceleration = a =?

Solution:

a = (v – u)/t = (50 – 20)/10 = 30/10 = 3 m s^-2

Acceleration of the object is 3 m s^-2

Q4. A stone is thrown vertically upwards with an initial velocity 50 m s^-1 comes to halt in 5 s. Find the acceleration.

Given: Initial velocity = u = 50 m s^-1, Final velocity = v = 0 m s^-1, Time elapsed = t = 5 s.

To Find: Acceleration = a =?

Solution:

a = (v – u)/t = (0 – 50)/5 = – 50/5 = – 10 m s^-2

The negative sign indicates retardation

Retardation of the stone is 10 m s^-2

Q5. The velocity of an object increases at a constant rate 54 km h^-1 to 72 km h^-1 in 5 s. Find the acceleration.

Given: Initial velocity = u = 54 km h^-1= 54 x (5/18) = 15 m s^-1, Final velocity = v = 72 km h^-1= 72 x (5/18) = 20 m s^-1, Time elapsed = t = 5 s.

To Find: Acceleration = a =?

Solution:

a = (v – u)/t = (20 – 15)/5 = 5/5 = 1 m s^-2

Acceleration of the object is 1 m s^-2

For More Topics in Motion in a Straight Line Click Here

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The post Concept of Acceleration appeared first on The Fact Factor.

In the last article we have studied the concept of distance travelled and displacement. Motion is an important part of our life. Our daily activities involve motion of different kinds. When we study motion, we come across another important concepts namely speed and velocity. In this article, we shall study the meaning of the two terms, there characteristics and distinguishing between them.

Notes
Very Short Answer Type Questions
Short Answer Type Questions
Essay Type Answer Questions
Concept Application

Speed:

Speed is defined as the rate at which the particle covers a distance along given path. Mathematically,

Speed = Distance/Time

It is denoted by v. Its S.I. unit is ms^-1 and c.g.s. unit is cm s^-1. Its dimensions are [L¹M⁰T^-1].

Instantaneous Speed:

The speed opf a particle at a given instant is known as instantaneous speed. The speddometer of a vehicle indicates instantaneous speed of the ehicle.

Uniform Speed:

A body is said to move with uniform speed if it covers equal distances in equal intervals of time throughout its motion.

Consider the motion of a car shown in above figure. In each equal interval of time of 1 minute, the car is covering equal distance of 300 m. Hence the car has uniform speed of 300 m min^-1. Thus instantaneous speed of the car is constant.

Non-Uniform or Variable Speed:

A body is said to move at a non-uniform speed if it covers unequal distances in the equal intervals of time.

Consider the motion of car shown in above figure. In each equal interval of time of 1 minute, the car is covering different distances. Hence the car has non-uniform or variable speed. Thus instantaneous speed of the car is changing with time.

Average Speed:

The ratio of the total distance travelled by the body to the total time of the journey is called average speed.

When a body is moving with uniform speed, then the instantaneous speed and average speed are equal.

Characteristics of Speed:

• The rate of change of distance with time is called the speed of the body.
• It is a scalar quantity
• Speed is always positive.
• In a circular motion, after executing a complete circle, the average velocity of the body is zero but its average speed is not zero.

Velocity:

The rate of change of displacement of a body with respect to time is called the velocity of the body. it is displacement of the body in unit time.

Velocity is a vector quantity, its S.I. unit is m/s and c.g.s. unit is cm/s.Its dimensions are [L¹M⁰T^-1]

Instantaneous Velocity:

For a body moving with non-uniform velocity, the velocity of the body at an instant is called instantaneous velocity.

Uniform Velocity: 

When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform velocity. Thus for body moving with uniform velocity, the instantaneous velocity is constant. Body has no acceleration,

For uniform motion acceleration, a = 0 and 

Displacement = velocity × time.

Example: The velocity of light in a particular medium is uniform velocity.  The velocity of sound in air at constant temperature is uniform velocity.

Non Uniform Velocity: 

When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have the nonuniform velocity or variable velocity. In this case body has acceleration.

A body can have non-uniform velocity in the following three cases.

• When the direction of the velocity of a body remains the same but its magnitude changes continuously then the body has variable velocity. e.g. a ball is thrown vertically upward.

When body is thrown vertically upward, the magnitude of velocity goes on decreasing but the direction of velocity remains the same (upward) till the body reaches the maximum height. At the highest point the velocity of the body is zero.

• When the magnitude of the velocity of a body remains the same but the direction changes continuously then the body has variable velocity. e.g. uniform circular motion of a body.

• When both the magnitude and direction of the velocity of body change continuously, then the body has variable velocity. e.g. ball thrown by making the acute angle with the horizontal (projectile motion)

When a body has variable velocity, then it has acceleration.

Average Velocity:

If the velocity of a body moving in particular direction changes with time, then the ratio of displacement to total time is called average velocity.

Characteristics of Velocity:

• The rate of change of displacement of a body with respect to time is called as the velocity of the body.
• It is a vector quantity.
• The velocity can be positive, negative or zero.
• In a circular motion, after executing a complete circle, the average velocity of the body is zero but its average speed is not zero.

Concepts:

Very Short Answer Type Questions

Q1, define the following.

• Speed: Speed is defined as the rate at which the particle covers a distance along given path.
• Instantaneous Speed: The speed opf a particle at a given instant is known as instantaneous speed.
• Uniform Speed: A body is said to move with uniform speed if it covers equal distances in equal intervals of time throughout its motion.
• Non-uniform Speed: A body is said to move at a non-uniform speed if it covers unequal distances in the equal intervals of time.
• Average Speed: The ratio of the total distance travelled by the body to the total time of the journey is called average speed.
• Velocity: The rate of change of displacement of a body with respect to time is called the velocity of the body.
• Instantaneous Velocity: For a body moving with non-uniform velocity, the velocity of the body at an instant is called instantaneous velocity.
• Uniform Velocity: When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform velocity.
• Non-uniform Velocity: When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have the nonuniform velocity or variable velocity.
• Average Velocity: If the velocity of a body moving in particular direction changes with time, then the ratio of displacement to total time is called average velocity.

Q2. Speedometer vehicle measures it’s ……… speed.

Speedometer vehicle measures it’s instantaneous speed.

Q3. When does a particle in motion have uniform speed?

A body is said to move with uniform speed if it covers equal distances in equal intervals of time throughout its motion.

Q4. The ratio of total distance travelled by a body to total time taken is known as its …….

The ratio of total distance travelled by a body to total time taken is known as its speed.

Q5. Give c.g.s., m.k.s. and S.I. units of speed, velocity.

Speed:

Velocity:

Q6. Convert following speeds ointo ms^-1.

Note: Conversion Factor: km h^-1x (5/18) = ms^-1

a) 18 km h^-1

18 km h^-1x (5/18) = 5 ms^-1

b) 63 km h^-1

63 km h^-1x (5/18) = 17.5 ms^-1

c) 99 km h^-1

99 km h^-1x (5/18) = 22.5 ms^-1

d) 108 km h^-1

108 km h^-1x (5/18) = 30 ms^-1

Q7. Convert following speeds ointo km h^-1.

Note: Conversion Factor: m s^-1 x (18/5) = km h^-1

a) 2 m s^-1

2 m s^-1x (18/5) = 7.2 km h^-1

b) 10 m s^-1

10 m s^-1x (18/5) = 36 km h^-1

c) 12.5 m s^-1

12.5 m s^-1x (18/5) = 45 km h^-1

d) 15 m s^-1

15 m s^-1x (18/5) = 54 km h^-1

Q8. When is the instantaneous speed is same as average speed?

When body is moving with uniform speed, then the instantaneous speed is same as average speed.

Q9. Which of the quantity, velocity or acceleration determines the direction of motion?

Velocity is the quantity which determines direction of the motion. The positive or negative sign of velocity indicated the direction of motion, while positive or negative sign of the acceleration merely indicates whether velocity is increasing or decreasing.

Q10. Give one example each type of following motions:

• Uniform velocity: Motion of light in vacuum
• Variable velocity: Motion of a train departing from station

Q11. Give an example of motion in which average speed is not zero, but average velocity is zero.

Uniform circular motion.

Short Answer Type Questions:

Q1. What are the characteristics of speed?

The characteristics of speed are as follows:

• The rate of change of distance with time is called the speed of the body.
• It is a scalar quantity
• Speed is always positive.
• In a circular motion, after executing a complete circle, the average velocity of the body is zero but its average speed is not zero.

Q2. What are the characteristics of velocity?

The characteristics of velocity are as follows:

• The rate of change of displacement of a body with respect to time is called as the velocity of the body.
• It is a vector quantity.
• The velocity can be positive, negative or zero.
• In a circular motion, after executing a complete circle, the average velocity of the body is zero but its average speed is not zero.

Q3. Distinguish between speed and velocity

Q4. Distinguish between uniform velocity and non-uniform velocity.

Q4. Explain the term ‘uniform velocity’ with suitable example.

When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform velocity. Thus for body moving with uniform velocity, the instantaneous velocity is constant. Body has no acceleration,

For uniform motion acceleration, a = 0 and 

Displacement = velocity × time.

Example: The velocity of light in a particular medium is uniform velocity.  The velocity of sound in air at constant temperature is uniform velocity.

Q5. Explain. “A particle moving with uniform speed can have variable velocity”.

In case of uniform circular motion a particle moves along the circumference of the circle with uniform speed. Thus the magnitude of the velocity of the particle is constant. In case of circular motion, the direction of the velocity at any instant is perpendicular to the position vector of the particle at that instant. Thus the velocity is along the tangent to the circular path at that instant. In circular motion the position of vector changes continuously, hence the direction of the velocity changes continuously. Thus in the case of uniform circular motion, the magnitude of velocity is constant but its direction is changing continuously. Thus it is variable velocity. Thus a particle moving with uniform speed can have variable velocity.

Essay Type Answer Questions

Q1. When can body have non-uniform velocity?

When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have the nonuniform velocity or variable velocity. In this case body has acceleration.

A body can have non-uniform velocity in the following three cases.

• When the direction of the velocity of a body remains the same but its magnitude changes continuously then the body has variable velocity. e.g. a ball is thrown vertically upward.

When body is thrown vertically upward, the magnitude of velocity goes on decreasing but the direction of velocity remains the same (upward) till the body reaches the maximum height. At the highest point the velocity of the body is zero.

• When the magnitude of the velocity of a body remains the same but the direction changes continuously then the body has variable velocity. e.g. uniform circular motion of a body.

• When both the magnitude and direction of the velocity of body change continuously, then the body has variable velocity. e.g. ball thrown by making the acute angle with the horizontal (projectile motion)

When a body has variable velocity, then it has acceleration.

Concept Application:

Q1. A body moving al;ong a straight path covers one third of a distance with velocity of 5 kmph and rest of the path with a velocity of 20 kmph. Find average speed of the body.

Let ‘x’ be the total distance travelled by the body

we have speed = distance / time

∴ time = distance/speed

Time taken for the first part of journey = t₁ = (x/3)/5 = x/15 hours

Time taken for the second part of journey = t₂ = (2x/3)/20 = x/30 hours

Total time taken = t₁ + t₂ = x/15 + x/30 = x/10 hours

Average speed = Distance travelled /Time

∴ Average speed = x / (x/10) = 10 kmph

Q2. A horse runs straight north and covers a distance of 5 m, then turns east and travels a distance of 12 m in total time of 5 s. Calculate the speed and the velocity of the horse.

Distance travelled = OA + AB = 5 m + 12 m = 17 m

Speed = Total distance travelled / Total time taken

∴ Speed = 17/5 = 3.4 ms^-1

By pythagoros theorem

OB² = OA² + AB² = 5² + 12² = 25 + 144 = 189

∴ Displacement = OB = √189 = 13.75 m from O to B

Velocity = Displacement/Time taken

∴ Velocity = 13.75/5 = 2.75 ms^-1 along vector OB

Q3. A bird sitting on a tree top at a height of 10 mfrom the ground to build a nest on the tree top. It starts picking up sticks lying below the tree at 9.00 a.m. and ends up at 9.20 a.m. During this interval it makes 10 trips up and down. Find the average speed and average velocity of the bird.

Total time taken = 9.20 a.m. – 9.00 a.m. = 20 min = 20 x 60 = 1200 s

Total distance travelled by the bird = 2 x height of tree x no. of trips

(Note 2 in the formula. It is for up and down in the trip)

∴ Total distance travelled by the bird = 2 x 10 x 10 = 200 m

Average speed = Distance travelled / Time

∴ Average speed = 200 /1200 = 1/6 = 0.167 ms^-1

Now, the bird is returning to its original position

Displacement = 0

∴ Average velocity = Displacement / Time = 0/1200 = 0

Q4. Find speed and velocity of a tip of minute hand of a clock 7 cm long a) in 15 minutes b) in half an hour c) in 1 hour.

a) in 15 minutes

The starting point of journey is P and the end point is at Q

Time taken = 15 min = 15 x 60 = 900 s

Distance travelled = Circumference/4 = 2πr/4 = πr/2

Distance travelled = 3.142 x 7 /2 = 11 cm

speed = distance /time = 11/900 = 0.012 cms^-1

Displacement = PQ = √2 r = 7√2 cm

Velocity = Displacement / Time = 7√2/900 = 0.011 cms^-1

b) in half an hour

The starting point of journey is P and the end point is at Q

Time taken = 30 min = 30 x 60 = 1800 s

Distance travelled = Circumference/2 = 2πr/2 = πr

Distance travelled = 3.142 x 7 = 22 cm

speed = distance /time = 22/1800 = 0.012 cms^-1

Displacement = PQ = 2r = 14 cm

Velocity = Displacement / Time = 14/1800 = 0.008 cms^-1

c) in 1 hour

The starting point of journey is P and the end point is at Q

Time taken = 1 hour = 60 min = 60 x 60 = 3600 s

Distance travelled = Circumference = 2πr

Distance travelled = 2 x 3.142 x 7 = 44 cm

speed = distance /time = 44/3600 = 0.012 cms^-1

Displacement = PQ = 0 cm

Velocity = Displacement / Time = 0/3600 = 0 cms^-1

Q5. A pencil is tied to one end of a string of length 14 cm and the other end is fixed to nail. If the time taken to draw a half circle and a full circle with the pencil is 2 s and 4 s, respectively. Find the speed and velocity (a) to draw a half circle and (b) to draw a full circle.

(a) to draw a half circle

The starting point of journey is P and the end point is at Q

Time taken = 2 s

Distance travelled = Circumference/2 = 2πr/2 = πr

Distance travelled = 3.142 x 14 = 44 cm

speed = distance /time = 44/2 = 22 cms^-1

Displacement = PQ = 2r = 28 cm

Velocity = Displacement / Time = 28/2 = 14 cms^-1

(b) to draw a full circle

The starting point of journey is P and the end point is at Q

Time taken = 4 s

Distance travelled = Circumference = 2πr

Distance travelled = 2 x 3.142 x 14 = 88 cm

speed = distance /time = 88/4 = 22 cms^-1

Displacement = PQ = 0 cm

Velocity = Displacement / Time = 0/4 = 0 cms^-1

Q6. A particle takes 8 s to travel from A to B through P and another particle travelling through Q takes 7 s. Find the speed and velocity of each particle.

a) Consider particle moving from A to B through P:

Time taken = 8 s

Distance travelled = AP + PB = 8 m + 6 m = 14 m

speed = distance /time = 14/8 = 1.75 ms^-1

Displacement = AB = 10 m

Velocity = Displacement / Time = 10/8 = 1.25 ms^-1

a) Consider another particle moving from A to B through Q:

Time taken = 7 s

Distance travelled = AQ + QB = 6 m + 8 m = 14 m

speed = distance /time = 14/7 = 2 ms^-1

Displacement = AB = 10 m

Velocity = Displacement / Time = 10/7 = 1.43 ms^-1

Q7. A particle takes 8 s to travel from A to B through P and another particle travelling through Q takes 10 s. Find the speed and velocity of each particle.

a) Consider particle moving from A to B through P:

Time taken = 8 s

Distance travelled = AP + PB = 9 m + 7 m = 16 m

speed = distance /time = 16/8 = 2 ms^-1

Displacement = AB = 10 m

Velocity = Displacement / Time = 10/8 = 1.25 ms^-1

a) Consider another particle moving from A to B through Q:

Time taken = 10 s

Distance travelled = AQ + QB = 6 m + 8 m = 14 m

speed = distance /time = 14/10 = 1.4 ms^-1

Displacement = AB = 10 m

Velocity = Displacement / Time = 10/10 = 1 ms^-1

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The motion of a body can be analyzed effectively by plotting different types of graphs. viz: Displacement-Time graph, Velocity-time graph, etc. In this article, we shall study Displacement-Time graphs and their interpretation.

Displacement – Time Graphs For Body at Rest:

Displacement – time graph shows the change in displacement of a body from a fixed point or the position with time. To draw an s–t graph, time is plotted along the x-axis, and displacement is plotted along the y – axis.

Displacement – Time Graph for a Stationary Body:

If the body is stationary or at rest, its position from a fixed point does not change with time.

a) The body has no initial displacement at t = 0:

Example: A bus stopped at a bus stop (reference point is the bus stop). In this case, the graph starts from the origin and continues along the x-axis

b) The body has an initial displacement at t = 0:

Example: A bus stopped at a point 5 m ahead of a bus stop (reference point is the bus stop). In this case, the displacement of the bus will remain 5 m for all instants of time. Thus s – t graph for a stationary body will start from s = 5m and is parallel to the x-axis

Displacement – Time Graphs For Uniform Motion

If a body travels equal distances in equal intervals of time, then the motion of the body is said to be a uniform motion. Thus, this graph is a straight line inclined to the x-axis.

Body is Moving in the Same Direction to Displacement with Uniform Velocity:

a) Body has no initial displacement at t = 0:

Example: A bus crossing a bus stop with uniform velocity 50 km h^-1 (reference point is the bus stop). In this case, the graph starts from the origin and is inclined to the x-axis.

b) Body has an initial displacement at t = 0

Example: A bus crossing a point 5 m ahead of a bus stop with uniform velocity 50 km h^-1 (reference point is the bus stop). In this case, the graph starts from s = 5 m and is inclined to the x-axis.

Body is Moving in Opposite Direction to Displacement with Uniform Velocity:

Here graph makes an obtuse angle with the positive direction of x-axis. Displacement decreases with time. The body is moving in opposite direction to its displacement. Example: The motion of a bus in its return journey.

Displacement – Time Graphs For Non Uniform Motion

Distance – Time graph for uniform acceleration:  

For such type of motion, the graph is a curved line and is parabolic in nature. It is observed that the steepness of the graph increases and therefore the slope as well as the speed (magnitude of velocity) increases. The slope of tangent at a point on the curve gives velocity of the body at that instant.

a) Body has no initial displacement at t = 0:

Example: Train departing from a railway station. (Reference point is the railway station)

b) Body has initial displacement at t = 0:

Example: Train which is at rest departing from a signal 5 km away from a railway station. (Reference point is the railway station)

Distance – Time graph for uniform retardation:

In this case also the graph is parabolic and curved but in opposite sense. In this case the steepness gradually decreases indicating uniform retardation. The slope of tangent at a point on the curve gives velocity of the body at that instant.

a) Body has no initial displacement at t = 0

b) Body has initial displacement at t = 0

Body is Moving in Opposite Direction to Displacement with Uniform Acceleration:

Body is Moving in Opposite Direction to Displacement with Uniform Retardation:

Importance of Displacement Time Graphs:

1. It helps to find position of a body at any instant during its journey.
2. Slope of tangent at point to the curve obtained gives instantaneous velocity of the body at that point.
3. Average velocity of the body can be obtained by finding the slope of the line joining the initial and final position of the body.
4. From the graph the nature and type of the motion of the body can be determined.

Concept Application

Q1. Draw a displaceent time graph for the following data with respect to a motion of particle. Interpret the type of motion.

The graph is as follows:

The nature of the graph (a curve) shows that the body is moving with non-uniform velocity and has uniform acceleration.

Q2. Draw a displaceent time graph for the following data with respect to a motion of particle. Interpret the type of motion.

The graph is as follows:

The nature of the graph (straight line) shows that the body is moving with uniform velocity.

Q3. Draw a displaceent time graph for the following data with respect to a motion of particle. Interpret the type of motion.

The graph is as follows:

The nature of the graph (a curve) shows that the body is moving with non-uniform velocity and has uniform retardation.

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Motion is an important part of our life. Our daily activities involve motion of different kinds. In this topic, we shall study the terminology of Mechanics, concept of motion and classification of motion.

• Notes
• Very Short Answer Type Questions
• Short Answer Type Questions
• Long Answer Type Questions
• Essay Type Answer Questions
• Concept Application

Terminology:

• Mechanics: The branch of physics which deals with the effects of forces on object is called mechanics. Mechanics is further classified into dynamics and statics.
• A Point Object: In the study of Mechanics we consider bodies or objects as particles or point objects. An object is said to be a point object if its dimensions are negligible as compared to the distance travelled by it. For example distance between stars is so large that for practical purpose those stars can be considered as particles or point objects.
• Body in Motion: A body is said to be in motion if it changes its position with respect to its immediate surroundings. It is to be noted that the motion of a body is a relative concept.
• Body at Rest: A body is said to be at rest if it does not change its position with respect to its immediate surroundings.
• Dynamics: The branch of physics (mechanics) which deals with the motion of the bodies and the forces causing it is called dynamics. It is further classified into kinematics and kinetics. Newton contributed a lot to dynamics by postulating his famous laws of motion.
• Kinematics: The branch of physics (mechanics) which deals with the motion of the bodies without considering the forces causing it is called kinematics. i kinematics measurement of time is essential.
• Kinetics: The branch of physics which deals with the motion of bodies considering cause of their motion.
• Statics: It is the branch of physics which deals with objects at rest or in equilibrium under the action of forces. the measurement of time is not essential in statics.

Motion: Meaning

The moving object is either a particle (by which we mean a point-like object such as an electron) or an object that moves like a particle (such that every portion moves in the same direction and at the same rate).

Motion of Living and Non Living Yhings:

Motion is characteristics of all living things. The movement of animals is called locomotion. Locomotion enables them to obtain food and to escape away from danger. Plants are fixed to substratum, hence they cannot locomate but they show movement. For example roots are geotropic while shoots are phototropic. The energy for movement of living things is derived from food which is metabolized in the body of living organism and energy is released.

Non-living things cannot move on their own, they are made to move. In this series of study of motion, we shall be considering motion of non-living things only.

A body is said to be in motion if it changes its position with respect to its immediate surroundings.

Motion is a Relative Concept:

The motion of a body is a relative concept. When we are specifying the motion it is with respect to some observer. Let us consider to persons say A and B in a lift moving upward. There is another person C standing outside the lift. Now though the lift is going up for A and B there is no change in positions with respect to each other thus they are at rest with respect to eachother. Thus for A and B, there is no motion with respect to each other but for both of them, C is moving downward. Now for C both A and B are moving upward. Hence motion is relative.

With respect to the earth surface, we may be at rest but we are moving about 100,000 km hr^-1 relative to sun.

Nothing in the universe is in absolute motion or is at absolute rest.

In order to know whether the position of an object changes with or not, a point absolutely fixed in space has to be chosen as reference point. All human bodies are moving in a space with respect to eachother. Hence they cannot be considered as reference point. Thus no such fixed reference point is available in the space. It means no object in universe is in state of absolute rest. As no object in universe is at absolute rest, so the absolute motion cannot be realized. Due to absence of absolute rest and absolute motion, only relative rest and relative motion can be realized.

Note: If two objects are moving in same direction on same straight line or two parallel straight lines then they are in relative motion only when they have different velocities.

Concept of Reference Frames:

A frame of reference is the frame in which the observer sits and maks observations. There is no rule or restriction on the choice of frame. We can choose a frame of reference to descibe the situation under study according to our convinience. For example, when we are travelling in a train then the compartment of the train in which we are travelling and bearth on you are sitting can be chosen as frame of reference.

There are two type of reference frames:

• Inertial Reference Frame: The frame of reference which is either at rest or moving with constant velocity is known as inertial frame of reference.
• Non-Inertial Reference Frame: A frame of reference moving with some acceleration is known as non-inertial reference frame.

Classification of Motion:

Classification of Motion on the Basis of Motion of Particles of a Body:

Motion can be classified into random motion, translational motion, rotational motion, and vibrational or oscillatory motion.

Random Motion:

In this motion particles move randomly in any possible direction and in any possible velocity. Thus, the path and the direction are not definite.

Example: Motion of gas molecules. Such random motion of molecules of gas is called molecular chaos.

Translational Motion:

In this motion every particle of the body has the same displacement.

The translational motion can be along straight line or along a curved path. Motion along a straight line is called a rectilinear motion  (e.g. motion of car in a straight line) and the motion of a body along a curved path is called curvilinear motion (e.g. the motion of a ball thrown in air, the motion of the earth around the Sun).

It is to be noted that in translatory motion, body does not change its orientation.

Rotational Motion:

In this motion the particles of body revolve in a circle about the same axis.

Examples: Motion of a fan, the motion of a wheel of moving vehicle, the motion of merry go round, etc.

Oscillatory or Vibrational Motion:

In this motion the body moves to and fro about a fixed point along the same path.

Examples: The motion of the bob of a pendulum, vibrating string of guitar, etc.

Classification of Motion on the Basis of Positional Reference Coordinates of Particles:

One Dimensional Motion:

The motion of an object is said to be one-dimensional if only one of the three coordinates specifying the position object changes with a time. In such motion the object moves in a straight line. This motion is also known as rectililnear motion or linear motion.

Example: Motion of a train along a straight track

Two Dimensional Motion:

The motion of an object is said to be two-dimensional if only two of the three coordinates specifying the position object changes with a time. In such motion the object moves along a plane.

Examples: Motion of planets around the sun, Motion of a car on curved flat road, circular motion, projectile motion, etc.

Three Dimensional Motion:

The motion of an object is said to be tree-dimensional if all the three coordinates specifying the position object changes with a time. In such motion the object moves in a space.

Example: A bir flying freely in the sky, a kite flying on windy day

Rectilinear Motion or One Dimensional Motion:

When a body moves along a straight-line path, its motion is called the one-dimensional motion or motion in a straight line or rectilinear motion. Example: the motion of a car along a straight road.

The Position of a Body or Particle:

 Assuming the direction of the motion along the x-axis, the path of one-dimensional motion can be represented by a straight line parallel to the x-axis then each point on the straight line represents the position of the particle at a different instant of time. The position of the particle at any instant can be specified by its x-coordinate. The x-coordinate changes with time.

Concepts:

Very Short Answer Type Questions

Q1. What is mechanics?

The branch of physics which deals with the effects of forces on object is called mechanics.

Q2. What are the different branches of mechanics?

Dynamics and statics are the different branches of physics.

Q3. What is kinematics?

The branch of physics (mechanics) which deals with the motion of the bodies without considering the forces causing it is called kinematics.

Q4. What is dynamics?

The branch of physics (mechanics) which deals with the motion of the bodies and the forces causing it is called dynamics.

Q5, What is kinetics?

The branch of physics which deals with the motion of bodies considering cause of their motion.

Q6. What is kinematics?

The branch of physics (mechanics) which deals with the motion of the bodies without considering the forces causing it is called kinematics.

Q7. What is statics?

It is the branch of physics which deals with objects at rest under the action of forces.

Q8. What is meant by “a body at rest”?

A body is said to be at rest if it does not change its position with respect to its immediate surroundings.

Short Answer Type Questions:

Q1. Explain what is meant by mechanics and what are its different branches?

The branch of physics which deals with the effects of forces on object is called mechanics. Mechanics is further classified into dynamics and statics.

Q2. Explain what is meant by dynamics and what are its different branches?

The branch of physics (mechanics) which deals with the motion of the bodies and the forces causing it is called dynamics. It is further classified into kinematics and kinetics.

Q3. Explain the concept of a ‘point object’.

In the study of Mechanics we consider bodies or objects as particles or point objects. An object is said to be a point object if its dimensions are negligible as compared to the distance travelled by it. For example distance between stars is so large that for practical purpose those stars can be considered as particles or point objects.

Long Answer Type Questions:

Q1. Explain “Motion is a relative concept”. OR Motion and rest are relative. How do you justify this?

The motion of a body is a relative concept. When we are specifying the motion it is with respect to some observer. Let us consider to persons say A and B in a lift moving upward. There is another person C standing outside the lift. Now though the lift is going up for A and B there is no change in positions with respect to each other thus they are at rest with respect to eachother. Thus for A and B, there is no motion with respect to each other but for both of them, C is moving downward. Now for C both A and B are moving upward. Hence motion is relative.

With respect to the earth surface, we may be at rest but we are moving about 100,000 km hr^-1 relative to sun.

Essay Type Answer Questions

Q1. How is motion classified on the basis of the movement of particles constituting the body?

Motion can be classified into random motion, translational motion, rotational motion, and vibrational or oscillatory motion.

• Random Motion: In this motion particles move randomly in any possible direction and in any possible velocity. Thus, the path and the direction are not definite. Example: Motion of gas molecules. Such random motion of molecules of gas is called molecular chaos.
• Translational Motion: In this motion every particle of the body has the same displacement. The translational motion can be along straight line or along a curved path. Motion along a straight line is called a rectilinear motion  (e.g. motion of car in a straight line) and the motion of a body along a curved path is called curvilinear motion (e.g. the motion of a ball thrown in air, the motion of the earth around the Sun).
• Rotational Motion: In this motion the particles of body revolve in a circle about the same axis. Examples: Motion of a fan, the motion of a wheel of moving vehicle, the motion of merry go round, etc.
• Oscillatory or Vibrational Motion: In this motion the body moves to and fro about a fixed point along the same path. Examples: The motion of the bob of a pendulum, vibrating string of guitar, etc.

Q2. How is motion classified on the basis of the change in representing coordinates of position of a body?

One Dimensional Motion:

The motion of an object is said to be one-dimensional if only one of the three coordinates specifying the position object changes with a time. In such motion the object moves in a straight line. This motion is also known as rectililnear motion or linear motion.

Example: Motion of a train along a straight track

Two Dimensional Motion:

The motion of an object is said to be two-dimensional if only two of the three coordinates specifying the position object changes with a time. In such motion the object moves along a plane.

Examples: Motion of planets around the sun, Motion of a car on curved flat road, circular motion, projectile motion, etc.

Three Dimensional Motion:

The motion of an object is said to be tree-dimensional if all the three coordinates specifying the position object changes with a time. In such motion the object moves in a space.

Example: A bir flying freely in the sky, a kite flying on windy day

Concept Application:

Q1. You are walking towards India Gate. Is India Gate at rest with respect to you or in motion with respect to you?

The motion of a body is a relative concept. When we are specifying the motion it is with respect to some observer. The India Gate is a structure fixed at one point and is at rest with respect to the ground (earth). Now as we start moving with repect to earth towards the India Gate, the distance between me and the India Gate decreases (position changes continuously) continuously with respect to me. Thus we can say that India Gate is in motion with respect to me.

Q2. A passenger seated in a train is at rest with respect to …….

The motion of a body is a relative concept. When we are specifying the motion it is with respect to some observer. A body is said to be at rest if it does not change its position with respect to its immediate surroundings. Thus, the passenger seated in a train is at rest with respect to other passengers seated in the train because his position at any instant is not changing with the other passengers seated in the train.

Q3. A passenger seated in a train is in motion with respect to …….

The motion of a body is a relative concept. When we are specifying the motion it is with respect to some observer. A body is said to be in motion if it changes its position with respect to its immediate surroundings. Thus, the passenger seated in a train is in motion with respect to objects outside the train (e.g. person on a platform) because his position at any instant is changing with the objects outside the train.

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Motion is an important part of our life. Our daily activities involve motion of different kinds. When a body moves along a straight-line path, its motion is called the one-dimensional motion or motion in a straight line or rectilinear motion. Example: the motion of a car along a straight road. When we study motion, we come across to important concepts namely distance travelled and displacement. In this article, we shall study the meaning of the two terms, there characteristics and distinguishing between them.

Notes
Very Short Answer Type Questions
Short Answer Type Questions
Essay Type Answer Questions
Concept Application

Distance:

The length of the path travelled by a body is called the distance travelled by it. The path of a body may not be straight. Distance is also referred as path length.

It is denoted by ‘s’ or ‘x’. Its S.I. unit is metre (m) and the c.g.s. unit is centimetre (cm). Its dimensions are [L¹M⁰T⁰]

Mathematically,

Characteristics of Distance:

• It is the length of the path followed by the object in a certain time. The path followed may or may not be along a straight line.
• It is a scalar quantity.
• It depends on the path followed by the object.
• It is always positive.
• It can be more than or equal to displacement.
• It may not be zero even if the displacement is zero.
• Distance between a given set of initial and final position can have infinite value.
• distance does not dectrease with time and never be zero for moving body.

Displacement:

The shortest distance from the initial position to the final position of the body is called the magnitude of the displacement.

It is a vector quantity whose direction is from initial position to final position. Its S.I. unit is metre (m) and the c.g.s. unit is centimetre (cm). Its dimensions are [L¹M⁰T⁰]

Mathematically

Characteristics of Displacement:

• It is the shortest distance between the initial position to the final position of the body. It is always along a straight line.
• It is a vector quantity whose direction is from the initial position to final position.
• It is independent of the path followed by the object.
• It may be positive, negative or zero.
• It may be equal but cannot be more than the distance travelled.
• It is zero when the distance travelled is zero.
• Displacement is not dependent on the choice of origin.
• The displacement of an object between two pints is the unique path that takes the body from its initial to final position.
• Displacement does not give any idea about the shape of path followed by the body to move between the two positions.
• The displacement between a given set of initial and final position have unique value.

Displacement Vector:

Position Vector of a Point:

Let us consider point P be in a space, whose coordinates are (x₁, y₁, z₁). Then its position vector w.r.t. origin O(0, 0, 0) is given as

Displacement Vector:

Let particle moves from point P with coordinates (x₁, y₁, z₁) to point Q with coordinates (x₂, y₂, z₂).

Then the displacement vector is given by

Concepts:

Very Short Answer Type Questions

Q1. Define distance.

The length of the path travelled by a body is called the distance travelled by it.

Q2.Define displacement.

The shortest distance from the initial position to the final position of the body is called the magnitude of the displacement.

Q3. Give c.g.s., m.k.s. and S.I. units of distance, displacement

Distance:

Displacement;

Q4. What are the dimensions of distance and displacement.

Dimensions of distance and displacement are the same [L¹M⁰T⁰]

Q5. When is the magnitude of displacement equal to its distance?

When an object moves in a straight line in the fixed direction without coming back, it’s displacement and distance magnitude will always be equal.

Short Answer Type Questions:

Q1. What are the characteristics of distance?

The characteristics of distance are as follows:

• It is the length of the path followed by the object in a certain time. The path followed may or may not be along a straight line.
• It is a scalar quantity.
• It depends on the path followed by the object.
• It is always positive.
• It can be more than or equal to displacement.
• It may not be zero even if the displacement is zero.

Q2. What are the characteristics of displacement?

The characteristics of displacement are as follows:

• It is the shortest distance between the initial position to the final position of the body. It is always along a straight line.
• It is a vector quantity whose direction is from the initial position to final position.
• It is independent of the path followed by the object.
• It may be positive, negative or zero.
• It may be equal but cannot be more than the distance travelled.
• It is zero when the distance travelled is zero.

Q3. Distinguish between distance and displacement.

Q4. Why is displacement referred to as a vector quantity and distance as scalar quantity?

Displacement is a vector quantity because it can be only described by using both magnitude as well as direction. while distanceis a scalar quantity, because it can be expressed completely by giving the length of the path (magnitude) taken by the body.

Q5. Explain “the displacement can be zero even if the distance is not zero”.

The length of the path travelled by a body is called the distance travelled by it, while The shortest distance from the initial position to the final position of the body is called the magnitude of the displacement. If a body, after travelling, comes back to its starting point, the displacement is zero but distance travelled is not zero.

Essay Type Answer Questions

Q1. Explain “displacement May be Positive or Negative or Zero”.

Case – 1: When Distance travelled and displacement are equal.

If an object moves along the positive direction of the x-axis through 4m and further moves by 3 m in the same direction. In this case, the distance travelled by the object is 7m and displacement is also 7 m.

Case – 2: When Distance travelled and displacement are not equal and displacement is positive

If an object moves along the positive direction of the x-axis through 4m and further moves by 3 m in the opposite direction. In this case, the distance travelled by the object is 7m and displacement is also + 1 m (along the positive direction of the x-axis).

Case – 3: When Distance travelled and displacement are not equal and displacement is negative

If an object moves along the positive direction of the x-axis through 3m and further moves by 4 m in the opposite direction. In this case, the distance travelled by the object is 7m and displacement is also – 1 m (along the negative direction of the x-axis).

Case – 4: When Distance travelled and displacement are not equal and displacement is zero

If an object moves along the positive direction of the x-axis through 4m and further moves by 4 m in the opposite direction. In this case, the distance travelled by the object is 8 m and the displacement is also 0 m.

Concept Application:

Q1. A body is first displaced by 5 m and then by 12 m in different directions. The minimum displacement it can have is …….. m.

The minimum displacement, the body can have = 12 m – 5 m = 7 m

Q2. A body is first displaced by 5 m and then by 12 m in different directions. The maximum displacement it can have is …….. m.

The maximum displacement, the body can have = 12 m + 5 m = 17 m

Q3. A cop gets information that a thief is 10 km away from the police station. Is it possible for cop to trace the thief with the given information?

This information is not sufficient as the direction in which the cop has to trace is not mentioned. The cop has to move along a circumference of a circle of radius 10 km through each and every point. At point T he can nab the thief. Thus, only specifying that a thief is 10 km away from the police station is not sufficient and it makes the task almost impossible. To trace the thief effectively with the distance direction also should be specified.

Thus for displacement both the magnitude and the direction is required. It is a vector quantity.

Q4. A horse is tied to a rope of length ‘r’ and the other end of the rope is tied to a pole. Find the displacement and the distance travelled by the horse in the following cases:

1. When the horse makes half revolution along a circular path.
2. When it makes one full revolution.
3. When it makes 3/4 th of the revolution.

When the horse makes half revolution along a circular path.

The starting point of journey is P and the end point is at Q

Distance travelled = Circumference/2 = 2πr/2 = πr units

Displacement = PQ = r + r = 2r units

When it makes one full revolution.

The starting point of journey is P and the end point is at Q

Distance travelled = Circumference = 2πr units

Displacement = PQ = 0 units

When it makes 3/4 th of the revolution.

The starting point of journey is P and the end point is at Q

Distance travelled = 3/4 x Circumference = 3/4(2πr) = 3πr/2 units

Applying Pythagoras theorem to Δ POQ

Displacement = PQ = √2 r units

Q6. A boy starts moving from a point in the north. after moving 5 m, he turns right and travels 2m straight, after which he again turns right. Finally he stops after travelling 5 m. What is the path length, he travels? Also find his displacement.

Path length =AB = BC + CD = 5 m + 2 m + 5 m = 12 m

Displacement = AD = 2 m

Q7. A particle moves 5 m towards the east and then moves 8 m towards the West. What is the total distance traveled and the magnitude of the displacement?

Distance travelled = OA + AB = 5m + 8 m = 13 m

Displacement = OB = 3 m towards the west

Q8. A horse runs straight north and covers a distance of 5 m, then turns east and travels a distance of 12 m. Draw the diagram showing the displacement and from the diagram, calculate distance travelled and displacement of the horse.

Distance travelled = OA + AB = 5 m + 12 m = 17 m

By pythagoros theorem

OB² = OA² + AB² = 5² + 12² = 25 + 144 = 189

Displacement = OB = √189 = 13.75 m from O to B

Q9. Redraw the following figure to scale and find out the distance and displacement of a particle moving along the path A-B-C-D.

Drawn to the scale on the graph paper

Scale 1 cm = 1m

Displacement = AD from A to D

Displacement = 9.8 m from A to D

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