The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.

If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the acceleration of the object.

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 (v = 0) | Zero | Stationary (at rest) | Zero |

- Question
Calculate the acceleration of the object represented by the steepest line in the graph.

change in velocity = (10 − 0) = 10 m/s

change in time = (2 − 0) = 2 s

acceleration = 10 ÷ 2

The displacement of an object can be calculated from the area under a velocity-time graph. The area under the graph can be calculated by:

- using geometry (if the lines are straight)
- counting the squares beneath the line (particularly if the lines are curved)

Calculate the total displacement of the object - its motion is represented by the velocity-time graph below.

Here, the displacement can be found by calculating the total area of the shaded sections below the line.

- Find the area of the triangle:
- Find the area of the rectangle:
- Add the areas together to find the total displacement: