Which of the following statements about average speed is correct? a. the average speed is equal to the magnitude of the average velocity. b. the average speed can never be greater than the magnitude of the average velocity. c. the average speed can never be less than the magnitude of the average velocity. d. if the average speed is zero, then the average velocity must be zero. e. if the average velocity is zero, then the average speed must be zero.

C. The average speed can never be less than the magnitude of the average velocity.

D. If the average speed is zero, then the average velocity must be zero.

Explanation:

First of all, let's remind the definition of average speed and average velocity:

- Average speed: it is the ratio between the distance covered and the time elapsed:

- Average velocity: it is the ratio between the displacement and the time elapsed:

- Let's also remind that the distance is always greater than the displacement (because the displacement just measure the distance in a straight line between the final point and the initial point of the motion, while the distance measures the whole path. Distance and displacement are equal only when the path is straight: otherwise, we always have

So let's now analyze each statement:

A. The average speed is equal to the magnitude of the average velocity. --> FALSE. Since distance and displacement are not always equal, this cannot be true.

B. The average speed can never be greater than the magnitude of the average velocity. --> FALSE. It's actually the opposite: since the distance is greater (or equal) than the displacement, the average velocity can never be greater than the average speed.

C. The average speed can never be less than the magnitude of the average velocity. --> TRUE. For what we said at the previous point.

D. If the average speed is zero, then the average velocity must be zero. --> TRUE. If the average speed is zero, it means that the total distance covered is zero, so the displacement must be zero as well.

E. If the average velocity is zero, then the average speed must be zero. --> FALSE. If the average velocity is zero, it means that the displacement is zero: however, in this case the distance can be different from zero (for example, in the case of a circular path), and so the average speed can be also non-zero.