Question

Sarah begins at a negative position along the x-axis. Sarah moves in the positive x-direction, turns around and then moves in the negative x-direction. Her final position is more negative that her initial position. Is the magnitude of Sarah's displacement greater than, less than, or equal to the distance she travels?

Answer 1

he magnitude of Sarah's displacement is less than the distance she travels

Explanation:

Hi!

The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.

So:

`displacement = |x_(final) -x_(initial)| \\distanceTraveled = 2|x_(return)-x_(initial)| + displacement\\`

Since all the terms are positive:

`x_(displacement)<x_(traveled)`