What does the gradient of a distance–time graph show?

speed. Distance divided by time is speed.

What does the area under a speed–time graph show?

distance. Speed multiplied by time is distance.

On a distance–time graph, what does a flat line mean?

stopped. The distance isn't changing.

A speed–time graph is a horizontal line at 10 m/s for 6 s. How far does the object travel?

60 m. The area is a rectangle: 10 × 6.

On a speed–time graph, what does a line sloping down show?

slowing down. The speed is decreasing.

Graphs of real situations · Edexcel IGCSE Mathematics A

In plain words

A graph can tell a story: a journey, a bath filling, a currency exchange. Reading one comes down to two things: what the steepness of the line means, and what the area under it means.

Three things to know

Distance–time graph: the gradient is the speed. A flat line means stopped; a steeper line means faster.
Speed–time graph: the gradient is the acceleration, and the area under the graph is the distance travelled.
A conversion graph is a straight line for changing one unit into another: read up from one axis and across to the other.

Worked example

A speed–time graph goes from 0 to 12 m/s in a straight line over 4 s, then stays at 12 m/s for 6 s. Find the total distance.

The distance is the area under the graph: a triangle and a rectangle.
Triangle: ½ × 4 × 12 = 24 m. Rectangle: 6 × 12 = 72 m.
Total = 96 m.

Tips and tricks

Read the axis labels first. The same shape means different things on a distance–time graph and a speed–time graph.
Gradient = change up ÷ change across. Read both from the scales, not by counting squares.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Graphs of real situations: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What does the gradient of a distance–time graph show?
- acceleration
- speed (the answer)
- distance
- time
Distance divided by time is speed.
What does the area under a speed–time graph show?
- speed
- acceleration
- distance (the answer)
- time
Speed multiplied by time is distance.
On a distance–time graph, what does a flat line mean?
- constant speed
- stopped (the answer)
- speeding up
- slowing down
The distance isn't changing.
A speed–time graph is a horizontal line at 10 m/s for 6 s. How far does the object travel?
- 16 m
- 30 m
- 60 m (the answer)
- 600 m
The area is a rectangle: 10 × 6.
On a speed–time graph, what does a line sloping down show?
- moving backwards
- slowing down (the answer)
- stopped
- constant speed
The speed is decreasing.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Graphs of real situations

Edexcel International GCSE Mathematics A 4MA1 · 7 marks · papermunch.org

Name ______________________________ Date ______________

On a distance–time graph, a line rises from 0 km to 30 km in half an hour. Find the speed.[2]
Show answerHide answer
60 km/h. 30 ÷ 0.5.
I got this one
State what a horizontal line shows on (a) a distance–time graph and (b) a speed–time graph.[2]
Show answerHide answer
(a) The object is not moving. (b) It is moving at a constant speed.
I got this one
A speed–time graph is a straight line from 20 m/s down to 0 in 5 s. Find the deceleration and the distance travelled.[3]
Show answerHide answer
4 m/s², and 50 m. 20 ÷ 5; ½ × 5 × 20.
I got this one

Answers: Graphs of real situations

1. 60 km/h. 30 ÷ 0.5.
2. (a) The object is not moving. (b) It is moving at a constant speed.
3. 4 m/s², and 50 m. 20 ÷ 5; ½ × 5 × 20.