Displacement, velocity and speed

The idea

Displacement and velocity are vectors: they have a direction, so they can be negative. Distance and speed are their sizes and are never negative. Average speed $= \frac{\text{total distance}}{\text{total time}}$ .

Choose a positive direction.
Displacement is final position minus starting position.
Distance adds up every part of the journey, whatever the direction.

Watch out Speed is never negative; a negative velocity means moving the other way.

See it worked

Worked example

A particle moves $5\text{ m}$ east, then $8\text{ m}$ west. Find its distance travelled and its displacement.

Distance: $5 + 8 = 13\text{ m}$ .
Taking east as positive, displacement $= 5 - 8 = -3\text{ m}$ .
So the displacement is $3\text{ m}$ west.

Answer Distance $13\text{ m}$ ; displacement $3\text{ m}$ west

Your turn

Question 1Non-calculator3 marks

A walker goes $300\text{ m}$ north, then $400\text{ m}$ east. Find the magnitude of the displacement.

Question 2Non-calculator3 marks

A cyclist travels $1200\text{ m}$ in $4$ minutes. Find the average speed in $\text{m s}^{-1}$ .

Question 3Non-calculator3 marks

A particle starts at position $x = 10\text{ m}$ and moves with constant velocity $-3\text{ m s}^{-1}$ for $4\text{ s}$ . Find its final position.

In past papers

10 official questions in 9 papers since 2018. The latest:

All A-level Maths past papers

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