Average Velocity Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following statement are correct?

1. The average speed can never be equal to the average velocity.
2. The average speed is always less than the average velocity.
3. The average speed is always greater than or equal to the average velocity.
4. The average speed is always equal to the average velocity.

Ans. The correct option is c. The average speed is always greater than or equal to the average velocity.

Explanation: Average speed of a body is given by the ratio of the total distance traveled by the body to the total time, while average velocity is the ratio of change in the position of the body to the total time taken. Since distance is always greater or equal to the magnitude of velocity, therefore, the average speed is always greater than or equal to the average velocity.

Ques. The speed of a body at a particular instant in time is known as

1. Average speed
2. Instantaneous speed
3. Unit speed
4. None of the above

Ans. The correct option is b. Instantaneous speed

Explanation: The instantaneous speed or velocity of a particle at a given instant of time is defined as the limit of average speed as the time interval becomes infinitesimally small.

Ques. Write the dimensional formula of average velocity.

Ans. Average velocity is given by the ratio of displacement of the body to the total time in which displacement occurs.

V_av = displacement/total time

The dimensional formula of average velocity is given by

[V_av] = [displacement]/[ time] = [M⁰LT⁰]/[M⁰L⁰T]

⇒ [V_av] = [M⁰LT^-1]

Ques. Is average velocity a scalar quantity or a vector quantity?

Ans. Average velocity is given by

V_av = displacement/total time

Since displacement is a vector quantity, therefore average velocity will be a vector quantity. Its value can be zero, positive, or negative.

Ques. What is the SI unit of average velocity?

1. m/s
2. m/s²
3. m²/s²
4. m²/s

Ans. The correct option is a. m/s

Explanation: Average velocity is given by

V_av = displacement/total time

The SI unit of displacement is meter (m) and time is second (s). Therefore, the SI unit of average velocity is meter-per-second (m/s).

Ques. Which device is used to measure the speed of the vehicle?

Ans. A speedometer is used in vehicles to measure their speed. It measures the instantaneous speed or magnitude of the instantaneous velocity i.e. speed of the vehicles at a specific instant of time.

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Short Answers Questions [2 Marks Questions]

Ques. Draw the velocity-time graph of a freely falling body.

Ans. The velocity-time graph of a freely falling body is a straight line with a positive slope to the time axis.

The initial velocity of a body when dropped from a certain height is zero. Then the velocity of the body goes on increasing due to the gravitational force of attraction of the surface of the earth, but the acceleration will be constant, which is known as acceleration due to gravity. Hence, a straight line with a positive slope with the time axis is observed in the velocity-time graph of a freely falling body.

Velocity-time graph of a free-falling body

Ques. Define average velocity.

Ans. Average velocity is defined as the change in the position or displacement of a particle divided by the time interval in which the displacement occurs.

The SI unit of average velocity is meters per second (ms^-1).

Ques. A truck driver drives 25 km down the road in 90 minutes. He then reverses and drives 8 km down the road in 30 minutes. What is his average velocity?

Ans. Net displacement of the truck, d = 24 - 8 = 16 km

Total time is taken, t = 90 + 30 = 120 minutes = 2 hours

The average velocity of the truck, V_av = net displacement/ total time

⇒ V_av = 16/2 = 8 km/hour

Ques. Define average speed.

Ans. The average speed is defined as the total distance traveled divided by the total time interval during which the motion occurs.

The SI unit of average speed is meters per second (ms^-1).

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Long Answers Questions [3 Marks Questions]

Ques. A man starts walking from a point on a circular field of a radius of 2 km and 2 hours later he finds himself at the same point where he initially started. Find

1. The average speed for the whole journey he traveled.
2. The average velocity of this man for the same.

Ans. Given the radius of the circular track, r = 2 km

Circumference of the circular track, S = 2ℼr = 2 x (22/7) x 2 = 12.57 km

Now if a man starts walking from a point and after some time it will return to the same point, then the total distance covered by the man will be equal to the circumference of the circular field.

Distance covered by man = Circumference of the field = 12.57 km

Since the man finally reaches the same point from where he started walking, therefore displacement of the man is zero.

• The average speed for the journey he traveled will be

Average speed = total distance traveled / total time taken = 12.57/2 = 6.28 km/hour

• Average velocity, Vav = net displacement / total time = 0

Ques. What are the differences between average speed and average velocity?

Ans. Followings are the difference between average speed and average velocity

Ques. A man walks 12 km east in 2 hours and then 3 km west in 1 hour. Calculate the average velocity of the man.

Ans. Net displacement of the man, d = 12 - 3 = 9 km

Total time is taken, t = 2 + 1 = 3 hours

The average velocity of the man, V_av = net displacement/ total time

⇒ V_av = 9/3 = 3 km/hour

Ques. A particle moves from A to B in a circular path of radius R covering angle θ as shown in the figure. Find the ratio of distance and magnitude of displacement of the particle.

Ans. From the figure, 

Distance = R sinθ/2 + R sinθ/2 = 2R sinθ/2

Displacement = Length of the arc AB = Rθ

Therefore, the ratio of distance to the magnitude of displacement of the particle is given by

distance/displacement = (Rθ)/(2R sinθ/2) = θ/(2sinθ/2)

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Very Long Answers Questions [5 Marks Questions]

Ques. A man covers a distance of 100 km with variable velocity. During the first half of his journey, his velocity was 20 km/h, and during the rest of his journey, his velocity was 40 km/h. Calculate the average velocity of the man during the whole course of his motion.

Ans. Given that the total distance covered by the man, S = 100 km

Let t be the time taken during the whole course of his motion.

During the first half of his journey

• Distance covered, S₁ = 100/2 = 50 km 
• Velocity, v₁ = 20 km/h
• Time taken, t₁ = S₁/v₁ = 50/20 = 5/2 hours

During the next half of his journey

• Distance covered, S₂ = 100/2 = 50 km 
• Velocity, v₂ = 40 km/h
• Time taken, t₂ = S₁/v₁ = 50/40 = 5/4 hours

Total time is taken, t = t₁ + t₂ = 5/2 + 5/4 = 15/4 hours

As the motion of the man is along the same direction, therefore

Average velocity, V_av = total distance traveled / total time taken

⇒ V_av = 100/(15/4) = 26.66 km/h

Ques. A car moves from city A to city B in a straight line and then comes back. While moving from A to B, it covers the first half of the distance at a rate of 40 km/h and the next half at 60 km/h. While moving from B to A, it moves at 40 km/h for the first half-time and 60 km/h for the remaining half-time. Find its average speed and magnitude of average velocity

1. During its motion from A to B
2. During its motion from B to A

Ans. Let the distance between A and B = 2x (in km)

1. During the motion from A to B

Let t be the time taken during motion from A to B.

During the first half of the journey

• Distance covered, S₁ = 2x/2 = x km 
• Speed, v₁ = 40 km/h
• Time taken, t₁ = S₁/v₁ = x/40 hours

During the next half of the journey

• Distance covered, S₂ = 2x/2 = x km 
• Velocity, v₂ = 60 km/h
• Time taken, t₂ = S₂/v₂ = x/60 hours

Total time is taken, t = t₁ + t₂ = x/40 + x/60 = x/24 hours

Average speed = total distance traveled / total time taken

⇒ Average speed = 2x/(x/24) = 48 km/h

As the motion of the car is along the same direction, therefore

Average velocity = Average speed = 48 km/h

2. During the motion from B to A

Let 2T be the total time taken during the motion from B to A.

During the first half-time of the journey

• Time is taken, t₁ = 2T/2 = T hour 
• Speed, v₁ = 40 km/h
• Distance covered, S₁ = v₁t₁ = 40T

During the first half-time of the journey

• Time is taken, t₂ = 2T/2 = T hour 
• Speed, v₂ = 60 km/h
• Distance covered, S₂ = v₂t₂ = 60T

Total distance traveled, S = S₁ + S₂ = 40T + 60T = 100T

Average speed = total distance traveled / total time taken

⇒ Average speed = 100T/2T = 50 km/h

As the motion of the car is along the same direction, therefore

Average velocity = Average speed = 50 km/h

Ques. A runner is running around a rectangle track with length = 30 meters and width = 15 meters. He travels around the rectangle track twice, finally running back to the starting point. If the total time he takes to run around the track is 100 seconds, determine average speed and average velocity.

Ans. Given

• Length of the rectangular track, l = 30 m
• Width of the rectangular track, w = 15 m

Perimeter of the track = 2(30 + 15) = 90 m

Since the runner moves 2 times around the track, therefore the distance traveled by the runner will be equal to two times the perimeter of the track i.e.

Total distance traveled, S = 2(perimeter of the track) = 2 x 90 = 180 m

The average speed of the runner = total distance traveled / total time

⇒ Average speed = 180 / 100 = 1.8 m/s

Since the runner finally reaches the same point, his net displacement will be zero. Therefore

Average velocity = net displacement / total time = 0

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