situations when the path length equals the magnitude of the displacement?

Question

For which one of the following situations will the pat length equal the magnitude of the displacement?
a)a jogger is running around a circular pth.
b) A ball is rolling down an inclined plane.
c) A train travels 5 miles east; and then, it stops and travels 2 miles west.
d) A ball rises and falls after being thrown straight up from the earth's surface.
e) a ball on the end of a string is moving in a vertical circle.

I'd rather you explain then give the answer....well if you'd be so kind...........thanks!!

Answer 1

The path length is going to be the total amount of ground you cover in a given interval. Displacement is the difference between the final and initial positions (vector) of a given interval. For example, the jogger running around the circular track of radius r, going around the track exactly once, travels a path length of 2rpi when done. His displacement, however, is 0 (his final position = original position). Thus, only when you travel in a straight line over the entire interval will the path length equal displacement. (That's b)