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

Part of

Velocity-time graphs show how the velocity of a moving object changes with time.

- Constant acceleration 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 |

The slope or gradient of a velocity-time graph =

= acceleration

The gradient of a velocity-time graph is the acceleration of the object.

The steeper the line the greater the acceleration.

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 =

= (40 m/s – 0 m/s) ÷ 10 s

= 40 m/s ÷ 10 s

= 4 m/s

^{2}The acceleration of the car in the first 10 s is 4 m/s

^{2}.

- Question
What is the acceleration of the car between 30 s and 50 s?

Acceleration is the gradient of the graph =

= (0 m/s – 60 m/s) ÷ 20 s

= -60 m/s ÷ 20 s

= -3 m/s

^{2}The car has an acceleration of -3 m/s

^{2}(or a retardation of 3 m/s^{2}).