Science > Physics > Motion in a Straight Line > Concept of Acceleration
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.
| c.g.s. unit | centimetre per second square (cm s-2) |
| m.k.s. unit | metre per second square (m s-2) |
| S.I. unit | metre per second square (m s-2) |
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.
| Acceleration | Retardation |
| The rate of change of velocity of a body with respect to time is called acceleration. | Negative acceleration is called retardation |
| Due to acceleration there is an increase in the velocity of the body. | Due to retardation there is a decrease in the velocity of the body. |
| Example: When train departs from station it has acceleration. | Example: When train halts at destination it has retardation. |
Q4. Distinguish between uniform acceleration and variable acceleration.
| Uniform Acceleration | Variable acceleration |
| The acceleration is said to be uniform (or constant) when equal changes in velocity take place in equal intervals of time. | If changes in velocity are not same in the same intervals of time, the acceleration is said to be variable. |
| Example — The motion of a body under gravity (e.g., free fall of a body) | Example — The motion of a vehicle on a crowded(or hilly) road. |
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