Velocity-time graphs - Higher
Velocity-time graphs show how the The distance travelled in one second in a specified direction. of a moving object changes with time.
What is shown on the velocity-time graph?
- Constant The rate of change of velocity is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. is shown by a straight rising line, A.
- Constant retardation (or deceleration) is shown by a straight falling line, C.
- Constant velocity is shown by a horizontal line, B.
- A horizontal line along the X-axis shows the speed is zero, meaning that the vehicle has stopped, or is stationary, D.
The table shows what each section of the graph represents:
| Section of graph | Gradient | Velocity | Acceleration |
| A | Positive | Increasing | Positive |
| B | Zero | Constant | Zero |
| C | Negative | Decreasing | Negative |
| D | Zero | Stationary (at rest, v = 0) | Zero |
| Section of graph | A |
|---|---|
| Gradient | Positive |
| Velocity | Increasing |
| Acceleration | Positive |
| Section of graph | B |
|---|---|
| Gradient | Zero |
| Velocity | Constant |
| Acceleration | Zero |
| Section of graph | C |
|---|---|
| Gradient | Negative |
| Velocity | Decreasing |
| Acceleration | Negative |
| Section of graph | D |
|---|---|
| Gradient | Zero |
| Velocity | Stationary (at rest, v = 0) |
| Acceleration | Zero |
The slope or gradient of a velocity-time graph =
\(\frac{\text{final velocity – initial velocity}}{\text{time taken}}\) = acceleration
Example
The velocity-time graph above is for a racing car accelerating from rest.
Question
What is the acceleration in the first 10 s?
Acceleration = the gradient of the graph = \(\frac{\text{final velocity – initial velocity}}{\text{time taken}}\)
= (40 m/s – 0 m/s) ÷ 10 s
= 40 m/s ÷ 10 s
= 4 m/s2
The acceleration of the car in the first 10 s is 4 m/s2.
Question
What is the acceleration of the car between 30 s and 50 s?
Acceleration is the gradient of the graph = \(\frac{\text{final velocity – initial velocity}}{\text{time taken}}\)
= (0 m/s – 60 m/s) ÷ 20 s
= -60 m/s ÷ 20 s
= -3 m/s2
The car has an acceleration of -3 m/s2 (or a retardation of 3 m/s2).