Describing Motion

To calculate the average speed of an object, you need to know the distance the object travelled and the time it took to travel that distance.

A mathematical equation in black script that defines speed. The equation reads: "Speed equals Distance travelled divided by Time".

A mathematical equation showing that speed (S) equals the distance (D) travelled divided by the time (T) taken.

  • S = Speed in metres per second (m/s)
  • D = Distance in metres (m)
  • T = Time in seconds (s)

Sometimes, you might be asked to calculate the distance or time, not just the speed. So, we need to know how to rearrange the formula to work out the various subjects.

The formula triangles below help us remember how to calculate speed, distance and time.

A set of three triangular diagrams illustrating the relationships between speed (S), distance (D), and time (T). The first triangle shows S at the base with D and T on the sides and an equation below it: S equals D divided by T. The second triangle highlights D with S and T on the sides and the equation: D equals S times T. The third triangle emphasises T with D and S on the sides and the equation: T equals D divided by S. Each highlighted variable is marked in pink.

Remember:

Physical QuantitySymbolUnitUnit Symbol
SpeedSMetres per secondm/s
DistanceDMetresm
TimeTSecondss

Example

Work out the speed of a jogger who ran 60 m in 20 s

60 m ÷ 20 s = 3 m/s

The speed = 3 m/s

The unit for speed is metres per second (m/s), which can be represented on a distance-time graph.

Distance-Time Graph

A distance-time graph plotted on a grid with time on the x-axis ranging from 0 to 700 and distance on the y-axis ranging from 0 to 350 metres. The graph starts with a straight incline indicating "Moving away from the start point at a steady speed". This is followed by a flat horizontal line denoting a "Stationary" period. The graph then declines in a straight line indicating "Moving back to the start point at a steady speed". A caption below the graph states, "A curved line will tell us it is changing speed". The graph illustrates various phases of motion with annotations provided in green boxes.

As shown in the graph, time (s) is plotted on the x-axis and distance (m) is plotted on the y-axis. The direction and slope of the lines tell us information about the speed of the object, as shown in the above graph.

Remember, the speed of the object is equal to the gradient of the line.

Relative motion

Relative motion takes into account both direction and speed. For example, sometimes when you are in a car that is driving at a fast speed and you look out of the window, the cars outside seem to be driving at a slow pace. However, in reality, all the cars are actually moving at a fast speed.

We need to know how to work out relative speed and the table below tells you how to do this:

SituationFormula for relative speed
Objects moving in an opposite direction towards or away from each otherAdd the two speed values together
Objects moving in the same direction towards or away from each otherFastest speed – slowest speed