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

Part of

When speed changes, the rate of change of speed can be calculated using the equation:

rate of change of speed =

Rate of change of speed is a scalar quantity and it is measured in m/s^{2}.

Speed-time graphs show how the speed of a moving object changes with time.

Gradient of speed-time graph = rate of change of speed (m/s^{2})

Area under speed-time graph = distance travelled (m)

Speed – Time Graph | |
---|---|

Gradient of graph | Rate of Change of Speed (m/s^{2}) |

Area under graph | Distance (m) |

This is a speed-time graph for a car moving between two sets of traffic lights.

- Question
What is the rate of change of speed of the car between 0 s and 10 s?

The rate of change of speed is the slope or gradient of the speed-time graph

rate of change of speed = gradient of the speed-time graph

=

rate of change of speed = (16 m/s – 0 m/s) ÷ 10 s = 1.6 m/s

^{2}

- Question
What is the rate of change of speed of the car between 20 s and 25 s?

The rate of change of speed = gradient of the speed-time graph =

The rate of change of speed = (0 m/s – 16 m/s) ÷ 5 s

= -3.2 m/s

^{2}.The car is slowing down at a rate of 3.2 m/s

^{2}.

- Question
What is the total distance between the two sets of traffic lights?

The total distance between the two sets of traffic lights = the total area under the graph.

There are 2 triangles and a rectangle. Find the area of each.

**From 0 s – 10 s**distance travelled = area of the triangle = ½ x 10 s x 16 m/s = 80 m.

**From 10 s – 20 s**distance travelled = area of the rectangle = 10 s x 16 m/s = 160 m.

**From 20 s – 25 s**distance travelled = area of the triangle = ½ x 5 s x 16 m/s = 40 m.

Total distance travelled = 80 m + 160 m + 40 m = 280 m.

- Question
What is the average speed of the car between the traffic lights?

Average speed =

average speed = 280 m ÷ 25 s = 11.2 m/s.