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

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Written by: Mark Curtis

Reviewed by: Dan Finlay

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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
- $speed = \frac{distance}{time} = \frac{rise}{run}$
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 $\frac{total distance travelled}{total time}$
- 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) 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 $\frac{rise}{run}$ for that bigger section

$\frac{rise}{run} = \frac{6}{1}$

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 $\frac{total distance travelled}{total time}$

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

$\frac{8}{1.75} = 4.57142 . . .$

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

Last updated: 17 October 2024

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