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.

The velocity of an object is its speed in a particular direction. Velocity is a vector quantity because it has both a magnitude and an associated direction. To calculate velocity, displacement is used in calculations, rather than distance.

Unlike distance, which is a scalar quantity, displacement is a vector quantity. It includes:

- the distance travelled, measured in a straight line from start to finish
- the direction of the straight line

When people run, fall, cycle or travel in a car or a plane their speed will change. They may speed up - acceleration, or slow down - deceleration. Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time. The change in velocity can be calculated using the equation:

The average acceleration of an object can be calculated using the equation:

This is when:

- acceleration (a) is measured in metres per second squared (m/s²)
- change in velocity (∆v) is measured in metres per second (m/s)
- time taken (t) for the change in velocity is measured in seconds (s)

If an object is slowing down, it is decelerating (and its acceleration has a negative value). Some typical values for acceleration in metres per second (m/s²) include:

Method of travel | Typical acceleration in m/s² |
---|---|

Running from a standing start | 6 |

Family car overtaking another car on a motorway | 4 |

Skydiver falling under the action of gravity | 10 |

Rollercoaster going into a loop | 30 - 60 |

Race car leaving the starting grid in a race | 14 |

A car takes 8.0 s to accelerate from rest to 28 m/s. Calculate the average acceleration of the car.

final velocity, (v) = 28 m/s

initial velocity, (u) = 0 m/s (because it was at rest - not moving)

change in velocity, (∆v) = (28 – 0) = 28 m/s

- Question
A car takes 25 s to accelerate from 20 m/s to 30 m/s. Calculate the acceleration of the car.

final velocity, (v) = 30 m/s

initial velocity, (u) = 20 m/s

change in velocity, (∆v) = (30 – 20) = 10 m/s

- Question
A bicycle is moving at 10 m/s when the rider applies the brakes and stops in 5 seconds. What is the acceleration?

final velocity, (v) = 0 m/s

initial velocity, (u) = 10 m/s

change in velocity, (∆v) = (0 − 10) = -10 m/s

The answer is a negative acceleration so the bicycle is

**decelerating**.