Under what condition(s) is the magnitude of average velocity of an object equal to its average speed? Under what condition(s) is the magnitude of average velocity of an object zero while its average speed is not zero?
The magnitude of average velocity of an object is equal to its average speed when the object moves along a straight line in a single direction. In this condition, the magnitude of displacement is exactly equal to the total distance travelled.
The magnitude of average velocity is zero while its average speed is not zero when the object returns to its starting point. In this case, the displacement is zero (since initial and final positions are the same), but the total distance travelled is greater than zero.
Explanation
According to the textbook context, average speed is calculated from the total distance travelled, whereas average velocity depends on displacement (change in position). For part (i), when an object moves in a straight path without changing direction, the distance travelled equals the magnitude of displacement, making average speed and the magnitude of average velocity equal. For part (ii), as illustrated by Example 4.2 (Sarang swimming to the other end and back), if an object comes back to its starting point, its displacement is zero, making average velocity zero. However, the total distance travelled is non-zero, so the average speed is not zero.