Displacement
Forces and Motion

Displacement

Glossary Definition for 16-19 IOP Glossary Project

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 Δr. In figure 2, Δ r = r2r1, where r1 and r2 are the position vectors of an object before and after the displacement, respectively. The components of the displacement vector Δ r are usually written Δx, Δy (and Δz, 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 = r2 − r1

where Δ r is the displacement between two points defined by the position vectors r1 and r2.

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.

Displacement
appears in the relation a=-(w^2)x F=-kx
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