Distance vs Displacement
The length of the journey versus the arrow from start to finish.
Lesson at a glanceShow the key points
- Distance is the length of the path actually travelled; it is a scalar.
- Displacement is the straight-line vector from the initial to the final position.
- |displacement| ≤ distance, with equality only for straight-line motion without turning back.
- After any round trip the displacement is zero.
- On a circle of radius R, after turning through θ: distance = Rθ, |displacement| = 2R sin(θ/2).
Your fitness tracker and a map app answer two different questions. One asks how far you walked; the other asks how far you are from where you started.
Two ways to measure a trip
Suppose a particle is at point A at time and at point B at time , travelling between them along some winding path. Two quantities describe this trip:
- The distance travelled is the length of the actual path from A to B.
- The displacement is the straight arrow from the starting point A to the finishing point B. Its size is the straight-line separation, and its direction is from start to finish.
Displacement has a magnitude and a direction. Does it also add by the triangle rule? Yes. Slide a coin across a table while someone pushes the table across the room, and the coin’s net displacement relative to the room is the vector sum of the two displacements. So displacement is a vector. Distance only has a size, so it is a scalar.
A jogger runs along a semicircular track of radius 50.0 m, from one end to the other. Find the distance covered and the displacement.
- 1Distance = length of the path; a scalar.
- 2Displacement = straight arrow from initial to final position; a vector.
- 3|displacement| ≤ distance, with equality only for straight-line motion that never turns back.
- 4Return to your starting point and your displacement is zero, however far you went.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.