Walk 300 m to the shop and 300 m back. You have covered a distance of 600 m, but your displacement is 0 m: you ended where you started.

• Distance is how far you travel. It has a size only, so it is a scalar.
• Displacement is how far you end up from the start, in a straight line, and in which direction. It has a size and a direction, so it is a vector.

Other pairs work the same way: speed (scalar) and velocity (vector), mass (scalar) and weight (vector, it points down).

Speed tells you how much distance you cover each second.

distance travelled = speed × time
s = v t

Distance in metres (m), time in seconds (s), speed in metres per second (m/s). Most real speeds change, so this gives the average speed over the trip.

Velocity is speed in a given direction. A car going round a roundabout at a steady 10 m/s has a constant speed, but its velocity keeps changing because its direction does.

Worth knowing roughly, because papers ask you to estimate: walking 1.5 m/s, running 3 m/s, cycling 6 m/s, a car on a motorway 31 m/s, sound in air 330 m/s.

Speeds in km/h have to become m/s before they go into an equation.

1. 72 km/h means 72 000 m in 3600 s
2. 72 000 ÷ 3600 = 20 m/s
3. Shortcut: divide km/h by 3.6

If your answer in m/s is bigger than the km/h number, you multiplied instead of dividing.