Question

Which of the following provides an example of one-dimensional motion in which average speed is not equal to the magnitude of average velocity?

a. A boy rides a bicycle along a straight path from his house to the market.

b. A pitcher throws a baseball along a perfectly straight line.

c. A man throws a ball vertically upwards and catches it when it falls back.

d. A girl walks 80m north, halts for a while, and walks 100m further north to reach home.

Answer 1

Average speed is a scalar quantity and is defined as the ration of total distance (scalar distance) to the total time taken.

Average velocity is a vector quantity and is defined as the ration of the displacement vector (vector quantity) to the total time taken.

Hence Average speed will be different from the average velocity only when the total distance covered by the particle is different from its displacement (displacement is the difference in final position and initial position).

In options a., b. and d. displacement is equal to the total distance. Because in all cases there is no change in the direction of the particle.

But in option c. the displacement is zero because initial position of the ball is equal to its final position. Hence average velocity is zero. The average speed wont be zero because the total distance is not zero. Hence in this case average velocity will be different than the average speed.