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

speed. Gradient is distance ÷ time, which is speed.

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

distance travelled. Speed × time is distance, and that is what the area is.

A speed–time graph is a straight line sloping downwards. What is the object doing?

slowing down steadily. A falling line means the speed is decreasing; straight means at a steady rate.

A speed–time graph goes from 4 m/s to 16 m/s in 3 s. What is the acceleration?

4 m/s². Gradient = (16 − 4) ÷ 3 = 4 m/s².

On a distance–time graph, line P is steeper than line Q. What does this show?

P is faster than Q. Steeper means more distance in the same time.

An object moves at a steady 5 m/s for 8 s. What area lies under its speed–time graph?

40 m. A rectangle 5 high and 8 wide: 5 × 8 = 40 m.

Distance–time and speed–time graphs · Cambridge IGCSE Co-ordinated Sciences (9

In plain words

A graph tells the story of a journey. On a distance–time graph the steepness is the speed: steep means fast, flat means stopped. On a speed–time graph the steepness is the acceleration, and the area underneath is how far you went.

Three things to know

On a distance–time graph the gradient is the speed. A flat line means stopped; a steeper line means faster.
On a speed–time graph the gradient is the acceleration and the area under the line is the distance travelled.
A curve on a speed–time graph means the acceleration is changing.

Worked example

A speed–time graph is a straight line from 0 to 12 m/s over 4 s. How far does the object travel?

Distance = the area under the graph, which here is a triangle.
Area = ½ × base × height = ½ × 4 × 12.
= 24 m.

Tips and tricks

Look at the axis label before anything else: distance or speed? A flat line means "stopped" on one and "steady speed" on the other.
For the area, split the shape into rectangles and triangles and add them up.

6 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Distance–time and speed–time graphs: 6 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 give?
- acceleration
- distance
- speed (the answer)
- time
Gradient is distance ÷ time, which is speed.
What does the area under a speed–time graph give?
- acceleration
- distance travelled (the answer)
- average speed
- force
Speed × time is distance, and that is what the area is.
A speed–time graph is a straight line sloping downwards. What is the object doing?
- moving at constant speed
- speeding up steadily
- slowing down steadily (the answer)
- standing still
A falling line means the speed is decreasing; straight means at a steady rate.
A speed–time graph goes from 4 m/s to 16 m/s in 3 s. What is the acceleration?
- 3 m/s²
- 4 m/s² (the answer)
- 12 m/s²
- 36 m/s²
Gradient = (16 − 4) ÷ 3 = 4 m/s².
On a distance–time graph, line P is steeper than line Q. What does this show?
- P travels further than Q.
- P accelerates more than Q.
- P is faster than Q. (the answer)
- P started before Q.
Steeper means more distance in the same time.
An object moves at a steady 5 m/s for 8 s. What area lies under its speed–time graph?
- 1.6 m
- 13 m
- 40 m (the answer)
- 64 m
A rectangle 5 high and 8 wide: 5 × 8 = 40 m.

6 questions

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

Worksheet

4 questions, 10 marks. Write your answers on paper, then check them.

Distance–time and speed–time graphs

Cambridge IGCSE Co-ordinated Sciences (9–1) 0973 · 10 marks · papermunch.org

Name ______________________________ Date ______________

A distance–time graph is a straight line from (0 s, 0 m) to (20 s, 300 m). Calculate the speed.[2]
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15 m/s. Gradient = 300 ÷ 20.
I got this one
A speed–time graph rises in a straight line from 0 to 12 m/s in 6.0 s. Calculate the distance travelled in that time.[3]
Show answerHide answer
36 m. Area of the triangle = ½ × 6.0 × 12.
I got this one
A car travels at a steady 20 m/s for 10 s, then slows steadily to rest in 5 s. Calculate the total distance travelled.[3]
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250 m. Rectangle 20 × 10 = 200 m, plus triangle ½ × 5 × 20 = 50 m.
I got this one
Describe the motion shown by a horizontal line on (a) a distance–time graph and (b) a speed–time graph.[2]
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(a) The object is not moving. (b) It is moving at a constant speed.
I got this one

Answers: Distance–time and speed–time graphs

1. 15 m/s. Gradient = 300 ÷ 20.
2. 36 m. Area of the triangle = ½ × 6.0 × 12.
3. 250 m. Rectangle 20 × 10 = 200 m, plus triangle ½ × 5 × 20 = 50 m.
4. (a) The object is not moving. (b) It is moving at a constant speed.