If the average velocity of a particle is zero and the average speed is not zero, what can be inferred about the motion of the particle?

When the average velocity of a particle is zero while the average speed is not zero, it indicates that the particle has moved around but ultimately returned to its initial position. Average velocity is defined as the displacement divided by the time taken, and a displacement of zero means that the starting and ending positions are the same.

At the same time, if the average speed is not zero, it indicates that the particle did cover some distance over the time in motion. This situation is commonly seen in scenarios where an object moves away from a point, changes direction, and then returns to that same point, resulting in a net displacement of zero but having traversed a path that involved actual movement. Hence, the implication is that the particle must have moved away and then come back, leading to the conclusion that it did return to its starting position.