Distance-time graphs show how the distance travelled by a moving object changes with time.

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A horizontal line on a distance-time graph shows that the object is stationary (not moving because the distance does not change)

A sloping line on a distance-time graph shows that the object is moving.

In a distance-time graph, the slope or gradient of the line is equal to the speed of the object. The steeper the line (and the greater the gradient) the faster the object is moving.

- Question
Calculate the speed of the object represented by the green line in the graph, from 0 to 3 s.

Calculate the average speed of the object represented by the green line in the graph, from 0 to 10 s.

Calculate the average speed of the object represented by the purple line in the graph, from 0 to 2 s.

Distance moved = (6 m – 0 m) = 6 m

time taken = (3 s – 0 s) = 3 s

speed = gradient of distance-time graph = distance moved ÷ time taken

speed = 6 m ÷ 3 s = 2 m/s

The total distance travelled by the vehicle on the green line is 7 m.

The time taken to travel this distance is 10 s.

Average speed = total distance moved ÷ time taken = 7 m ÷ 10 s = 0.7 m/s.

The speed of the object represented by the purple line can also be calculated.

distance moved = (10 m – 0 m) = 10 m

time taken = (2 s – 0 s) = 2 s

speed = gradient of distance-time graph = distance moved ÷ time taken

speed = 10 m ÷ 2 s = 5 m/s