Displacement | Learn Physics with Erkan Koymen

Definition

Displacement is the change in an object’s position.

It is represented by a vector drawn from the initial position to the final position.

Unlike distance, displacement depends only on where the motion starts and where it ends. The actual path taken is not important.

The SI unit of displacement is the meter (m).

In one-dimensional motion,

Displacement = Final Position − Initial Position

\Delta x = x_f – x_i

where

x_i = \text{initial position}

x_f = \text{final position}

\Delta x = \text{displacement}

A positive displacement indicates motion in the positive direction, while a negative displacement indicates motion in the opposite direction.

Example

An object moves from x = −4 m to x = +5 m.

\Delta x = +5 – (-4) = +9\,\mathrm{m}

The displacement is +9 m, meaning the object’s final position is 9 m in the positive direction relative to its initial position.

Distance tells how much ground an object has covered.

Displacement tells how far and in which direction the object’s position has changed.

An object may travel a long distance but have a small displacement—or even zero displacement if it returns to its starting position.

Example 1: Comparing Distance and Displacement

Motion

Distance

Distance = 3m + 4m = 7m

Displacement

The displacement is the straight-line vector from the starting point to the final point.

|\Delta \vec{r}| = \sqrt{3^2 + 4^2} = 5\,\mathrm{m}

\text{Direction: } 53^\circ \text{ north of east}

Distance = 7 m
Displacement = 5 m, 53^onorth of east

Example 2: Zero Displacement

A runner completes one full lap on a circular track.

Distance = 400 m

Displacement

The runner finishes at the same position where the motion started.

|\Delta \vec{r}| = 0\,\mathrm{m}

Distance = 400 m
Displacement = 0 m

An object can travel a large distance while having zero displacement if it returns to its starting position.