## Displacement

Glossary Definition for 16-19

#### Description

Displacement is a vector quantity; it describes the difference in position between two points, measured from one to the other. Referring to **figure 1**, the displacement from A to B is defined by a vector in the direction of the straight line from A to B, with magnitude equal to the distance between A and B measured along that line.

*Figure 1: The distance travelled and displacement in moving from point A to point B along a curved path*

When dealing with motion in one dimension along a straight line, displacement is usually represented by the symbol s. When considering coordinate systems in two or three dimensions, displacement is usually represented by the symbol Δ**r**. In **figure 2**, Δ ** r** =

**r**_{2}–

**r**_{1}, where

**r**_{1}and

**r**_{2}are the position vectors of an object before and after the displacement, respectively. The components of the displacement vector Δ

**are usually written Δ**

*r**x*, Δ

*y*(and Δ

*z*, if in three dimensions).

*Figure 2: The change in displacement in moving from point 1 to point 2*

#### Discussion

If the motion between the start and the new position is not along a straight line, the displacement is less than the overall distance travelled. See **figure 1**. In the special case that the motion returns to its original position, the displacement is zero although the distance travelled is not.

For one-dimensional motion along a straight line, direction may be described, e.g. as ‘to the left/right’ or ‘up/down’. If one direction is defined as positive, then displacement in the opposite direction is negative. For example, if ‘right’ is positive, then a displacement of +4 m means 4 m to the right, and –6 m means 6 m to the left of the starting point.

#### SI Unit

metre, m

#### Expressed in SI base units

m

#### Other commonly used unit(s)

kilometre, km; mile, mi

#### Mathematical Expressions

Δ ** r** =

**r**_{2}−

**r**_{1}

where Δ ** r** is the displacement between two points defined by the position vectors

**r**_{1}and

**r**_{2}.

#### Related entries

- Distance
- Velocity

#### In context

Starting and ending at the same point, an athlete may run a distance of 400 m along the inside lane of a running track, but the displacement of the finishing position with respect to the starting position will be zero.