2.2 Distance and Displacement

Key Concepts

Distance

The length of the path traveled between two positions.

  • Scalar quantity (no direction)
  • Denoted by Δx, Δr, Δs, Δd, or Δl
  • SI unit: metre (m)

Displacement

The shortest distance from the initial position to the final position (straight directed distance).

  • Vector quantity (has direction)
  • Change in position vector Δd
  • SI unit: metre (m)

Mathematical Representation

Displacement:

Δd = d₂ - d₁

Where:

  • Δd: change in position (displacement)
  • d₂: final position
  • d₁: initial position

Point to Ponder

The symbol Δ (Greek letter delta) is used to represent a 'change in' any quantity. For example, elapsed time Δt is the difference between the ending time t₂ and beginning time t₁:

Δt = t₂ - t₁

Can You Tell?

If on a 400 m running track your starting point and ending point are the same, how much distance have you covered? What is your displacement?

  • Distance covered: 400 m
  • Displacement: 0 m (starting point = ending point)

Can displacement be greater than distance? Can distance and displacement be equal?

  • Displacement cannot be greater than distance.
  • Distance and displacement can be equal when moving in a straight line.