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Distance-Time Graphs (Cambridge (CIE) IGCSE Maths)

Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Cambridge (CIE) Maths: CoreEdexcel Maths A (Modular): Higher Unit 1Cambridge (CIE) Maths: ExtendedEdexcel Maths A: Higher

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Distance-Time Graphs

How do I use a distance-time graph?

  • Distance-time graphs show the distance travelled at different times

    • Distance is on the vertical axis

    • Time is on the horizontal axis 

  • The gradient of the graph is the speed

    • speed space equals space distance over time space equals space rise over run

  • The steeper the line the faster the object is moving

    • Lines with positive gradients represent objects moving away from the start point

    • Lines with negative gradients represent objects moving towards the start point

    • Lines that are horizontal represent rest

      • The object is stationary (not moving)

How do I work out the overall average speed?

  • For journeys with multiple parts

    • the overall average speed for the whole journey is fraction numerator total space distance space travelled over denominator total space time end fraction

    • The total time includes any rests

Examiner Tips and Tricks

These questions often have a lot of parts that depend on each other, so always double check each answer before continuing.

Worked Example

One afternoon, Mary cycled 8 km from her home to her grandfather's house.
Part of the travel graph for her journey is shown. 

A distance time graph

 (a) Find Mary's speed at 2 pm.

The speed is the gradient of the line at that point
The gradient at 2pm is the same as the gradient for all points between 1:45pm and 2:45pm
It is easiest to use rise over run for that bigger section

rise over run equals 6 over 1

6 km/h

(b) Calculate, in minutes, how long Mary stopped on the way to her grandfather's house.

The horizontal line is where Mary stops
The scale is 1 square = 15 minutes

15 minutes

(c) Calculate Mary's overall average speed from leaving her home to arriving at her grandfather's house, giving your answer correct to 3 significant figures.

 Overall average speed is fraction numerator total space distance space travelled over denominator total space time end fraction 

Total distance travelled is 8 km
Total time (including rests) is 1.75 hours

fraction numerator 8 over denominator 1.75 end fraction equals 4.57142...

Round the answer to 3 significant figures

4.57 km/h (to 3 s.f.)

(d) Mary stayed at her grandfather's house for half an hour, then cycled home at a steady speed without stopping, arriving home at 4pm.

Complete the travel graph for Mary's journey.

Rest is a horizontal line
Returning home is a straight line with a negative gradient 

Example-5-3-20-Diagram-2, IGCSE & GCSE Maths revision notes

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    Author
    Reviewer
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.