The graph below shows a velocity - time
graph for the motion of a particle. The motion has three stages.

Stage 1. The particle travels from rest with constant accleration for t=

Stage 2. The particle travels at constant velocity from t =

Stage 3. The particle travels with constant deceleration until it stops at time t=

The area under the graph represents the total distance travelled.

Find the total distance travelled in these cases:

1 When constant acceleration = 1 ms

2 When constant acceleration = 1.5 ms

Stage 1. The particle travels from rest with constant accleration for t=

**seconds.***t1*Stage 2. The particle travels at constant velocity from t =

**to t=***t1***seconds.***t2*Stage 3. The particle travels with constant deceleration until it stops at time t=

**.***t3*The area under the graph represents the total distance travelled.

Find the total distance travelled in these cases:

1 When constant acceleration = 1 ms

^{-2}, t1 = 3 seconds, t2 = 6 seconds, t3 = 9 seconds.2 When constant acceleration = 1.5 ms

^{-2}, t1 = 4 seconds, t2 = 6 seconds, t3 = 12 seconds.## Summary/Background

Answers: 1. 18 m, 2. 42 m

## Software/Applets used on this page

Uses Cinderella interactive geometry

## Glossary

### acceleration

the rate of change of velocity with time. It is a vector quantity with magnitude and direction.

### constant

a value in a formula or equation that cannot change.

### deceleration

negative acceleration, also known as retardation

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### particle

an object with negligible size and internal structure, which can be represented by a point; the fundamental assumption in mechanics.

### velocity

the rate of change of displacement. It is a vector quantity with magnitude and direction.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | M1 | Kinematics | Velocity-time graphs | - |

AQA AS Maths 2017 | Mechanics | Kinematics and Units | Velocity-Time Graphs | - |

AQA AS/A2 Maths 2017 | Mechanics | Kinematics and Units | Velocity-Time Graphs | - |

CCEA A-Level (NI) | M1 | Kinematics | Velocity-time graphs | - |

CIE A-Level (UK) | M1 | Kinematics | Velocity-time graphs | - |

Edexcel A-Level (UK - Pre-2017) | M1 | Kinematics | Velocity-time graphs | - |

Edexcel AS Maths 2017 | Mechanics | Constant Acceleration Motion | Velocity-Time Graphs | - |

Edexcel AS/A2 Maths 2017 | Mechanics | Constant Acceleration Motion | Velocity-Time Graphs | - |

OCR A-Level (UK - Pre-2017) | M1 | Kinematics | Velocity-time graphs | - |

OCR AS Maths 2017 | Mechanics | Units and Motion Basics | Velocity-Time Graphs | - |

OCR MEI AS Maths 2017 | Mechanics | Working with Motion | Velocity-Time Graphs | - |

OCR-MEI A-Level (UK - Pre-2017) | M1 | Kinematics | Velocity-time graphs | - |

Pre-U A-Level (UK) | Mech | Kinematics | Velocity-time graphs | - |

Universal (all site questions) | K | Kinematics | Velocity-time graphs | - |

WJEC A-Level (Wales) | M1 | Kinematics | Velocity-time graphs | - |