Distance-time graphs

A distance-time graph is a useful way to represent the motion of an object. It shows how the distance moved from a starting point changes over time.

Distance-time graph displaying purple line travelling at steady speed, and green line travelling at steady speed, stationary for 3 seconds, then moving again at steady speed.Example of a distance-time graph

In a distance-time graph:

  • distance travelled is plotted on the vertical (y) axis
  • time taken is plotted on the horizontal (x) axis

The gradient of the line is equal to the speed. This means that the line is:

  • horizontal for a stationary object (because the distance stays the same)
  • a straight diagonal for an object moving at a constant speed

The steeper the line, the greater the gradient and the greater the speed.

British Cycling coach Charlie Evans talks about how distance-time graphs are used in cycling

Example 1

Question

From the distance-time graph above, calculate the speed represented by the green line between 6 s and 10 s.

distance travelled = 7 – 6 = 1 m

time taken = 10 – 6 = 4 s

speed = 1 ÷ 4 = 0.25 m/s

Example 2

Question

From the distance-time graph above, calculate the average speed represented by the green line between 0 s and 10 s.

distance travelled = 7 m

time taken = 10 s

speed = 7 ÷ 10 = 0.7 m/s