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 A quantity that requires only a size, for example, distance travelled is 20 m. 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.
Summary
| Speed – Time Graph | |
| Gradient of graph | Rate of Change of Speed (m/s2) |
| Area under graph | Distance (m) |
| Gradient of graph | |
| Speed – Time Graph | Rate of Change of Speed (m/s2) |
| Area under graph | |
| Speed – Time Graph | Distance (m) |
Example
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.