If an object moves through a nonzero distance, can it have zero displacement? Give one supporting example.

What the question is really asking

You are comparing two different ways to describe motion: how much ground an object covers versus how far it ends up from where it started.

Distance versus displacement

• Distance is the total path length traveled. It is always nonnegative.
• Displacement is the change in position, including direction. In one dimension:

$$\text{displacement} = x_f - x_i$$

So displacement can be zero even when distance is not.

When displacement becomes zero

Displacement is zero exactly when the final position equals the initial position:

$$x_f = x_i \Rightarrow x_f - x_i = 0$$

This happens on any round trip, loop, or back-and-forth motion that returns to the start.

Example that supports the answer

Start at a point on a straight line.

• Walk $10\,\text{m}$ east, then $10\,\text{m}$ west.
• Total distance traveled:

$$10 + 10 = 20\,\text{m}$$

• Displacement:

$$x_f - x_i = 0\,\text{m}$$

You moved, so the distance is not zero, but you ended where you began, so the displacement is zero.