Rate of change of speed

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

rate of change of speed = \frac{\text{final speed – initial speed}}{\text{time taken}}

Rate of change of speed is a scalar quantity and it is measured in m/s2.

Speed-time graphs

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

curriculum-key-fact
Gradient of speed-time graph = rate of change of speed (m/s2)
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Area under speed-time graph = distance travelled (m)

Summary

Speed – Time Graph
Gradient of graphRate of Change of Speed (m/s2)
Area under graphDistance (m)

Example

A speed-time graph for a car moving between two sets of traffic lights

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

= \frac{\text{final speed – initial speed}}{\text{time taken}}

rate of change of speed = (16 m/s – 0 m/s) ÷ 10 s = 1.6 m/s2

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 = \frac{\text{final speed – initial speed}}{\text{time taken}}

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

= -3.2 m/s2.

The car is slowing down at a rate of 3.2 m/s2.

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 = \frac{\text{total distance moved}}{\text{time taken}}

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