Speed-time graph: (0, 0) (2, 10) (6, 10) (8, 16) (12, 0), find the… Step by Step

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The question

Question: the speed-time graph joins (0, 0) (2, 10) (6, 10) (8, 16) (12, 0), find the distance.

speed-time graph: (0, 0) (2, 10) (6, 10) (8, 16) (12, 0)

1 Read the graph

Across: the time.

Up: the speed, in m/s.

Going up: speeding up.

Flat: a steady speed.

Going down: slowing down.

2 Distance = area

The distance is the area under a speed-time graph.

Speed times time is a rectangle; a steady speed-up is half a rectangle.

distance = area under the graph

Under part A: a triangle.

Half of 2 times 10 is 10.

A: area = ½ × 2 × 10 = 10

Under part B: a rectangle, 4 across and 10 up.

4 times 10 is 40.

B: area = 4 × 10 = 40

Under part C: a rectangle and a triangle.

2 × 10 + a half × 2 × 6: 26.

C: area = 2 × 10 + ½ × 2 × 6 = 26

Under part D: a triangle.

Half of 4 times 16 is 32.

D: area = ½ × 4 × 16 = 32

Careful!

16 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 16 m ✗

3 Add the areas

All the parts together: 108 m.

distance = 10 + 40 + 26 + 32 = 108 m

4 Check

Let's check: the average speed is 9 m/s.

That is between 0 and the top speed, 16.

So the answer makes sense!

average speed = 108 ÷ 12 ≈ 9 m/s: between 0 and 16

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer