What type of motion does a particle undergo if its average speed is greater than its average velocity?

When a particle's average speed is greater than its average velocity, it indicates that the particle is changing direction frequently, which is characteristic of back-and-forth motion. Average speed measures the total distance traveled divided by the total time taken, while average velocity is the total displacement (the straight-line distance from the starting point to the ending point) divided by the total time taken.

In scenarios where a particle moves back and forth, it can cover a larger distance while the displacement remains relatively smaller, leading to a higher average speed compared to its average velocity. For example, if a particle travels to the right and then returns to the starting point, it could have a significant distance traveled (thus a high average speed) but a displacement of zero, resulting in a lower average velocity.

In contrast, a particle moving in a straight line would not exhibit this discrepancy between average speed and average velocity, since its distance traveled would equal its displacement. Uniform acceleration doesn't necessarily imply that speed will exceed velocity as both values can change simultaneously depending on the path taken. Lastly, if the particle is at rest, both average speed and average velocity would be zero, eliminating the possibility of one being greater than the other.