Distance and Displacement

Distance is the actual length of the path travelled by an object between two instants of time — it is a scalar, and because it only ever accumulates as an object moves, distance travelled is never negative and never decreases with time.

Displacement is the difference between an object's final and initial positions over a given time interval — equivalently, the straight-line (shortest) distance between the initial and final positions, directed from the initial position to the final position. Displacement is a vector.

A few consequences worth keeping straight, since they are easy to mix up:

1. Distance travelled is always positive (never negative or zero, unless the object doesn't move at all).
2. Displacement can be positive, negative, or zero, depending on where the object ends up relative to where it started — even after travelling a large distance, an object that returns to its starting point has zero displacement.
3. The magnitude of displacement can be equal to or less than, but is never greater than, the distance travelled (a straight path makes them equal; any curving or backtracking makes distance the larger of the two). …