Science > Physics > Motion in a Straight Line > Concept of Speed and Velocity
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:
| c.g.s. unit | centimetre per second (cm s-1) |
| m.k.s. unit | metre per second (m s-1) |
| S.I. unit | metre per second (m s-1) |
Velocity:
| c.g.s. unit | centimetre per second (cm s-1) |
| m.k.s. unit | metre per second (m s-1) |
| S.I. unit | metre per second (m s-1) |
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
| Speed | Velocity |
| The rate of change of distance with time is called the speed of the body. | The rate of change of displacement of a body with respect to time is called as the velocity of the body. |
| Speed = Distance / Time | Velocity = Displacement / Time |
| It is a scalar quantity | It is a vector quantity. |
| Speed is always positive. | The velocity can be positive, negative or zero. |
Q4. Distinguish between uniform velocity and non-uniform velocity.
| Uniform Velocity | Non-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. | 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. |
| The instantaneous velocity is constant. | The instantaneous velocity is not constant. |
| Body possesses no acceleration | Body possesses acceleratiion |
| Net forces acting on body are zero. | Net force acting on body are not zero. |
| Example: The velocity of light in a particular medium | Example: The velocity of train departing from station. |
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