Distance travelled

Displacement is measured as the crow flies. In many cases, it is more adequate to quantify the distance travelled, which is the length of path followed by a particle.

The distance travelled differs from displacement in many ways. Whilst displacement is a vector, the distance travelled is a scalar. Displacement is measured as the crow flies: its magnitude only depends of the starting position and the end position, irrespective of the actual path in between. By contrast, the distance travelled is always measured along the actual path.

Example: cars race round a circular track. When a car has travelled exactly half a lap, the magnitude of its displacement is the diameter of the circle (the length of the straight line from starting point to endpoint), whilst the distance travelled by it is half the circumference of the circle (the length of the actual path, which is half a circle). When it has travelled exactly one lap, its displacement is zero (the final position is the same as the initial one), whereas the distance travelled is the circumference of the circle.

Note: above, we referred to the ‘magnitude of the displacement’. This is because displacement is a vector.