Speed-time graph: (0, 0) (5, 25) (10, 25) (15, 10) (20, 0), find the… Step by Step

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The question

Question: the speed-time graph joins (0, 0) (5, 25) (10, 25) (15, 10) (20, 0), find the distance.

speed-time graph: (0, 0) (5, 25) (10, 25) (15, 10) (20, 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 5 times 25 is 62.5.

A: area = ½ × 5 × 25 = 62.5

Under part B: a rectangle, 5 across and 25 up.

5 times 25 is 125.

B: area = 5 × 25 = 125

Under part C: a rectangle and a triangle.

5 × 10 + a half × 5 × 15: 87.5.

C: area = 5 × 10 + ½ × 5 × 15 = 87.5

Under part D: a triangle.

Half of 5 times 10 is 25.

D: area = ½ × 5 × 10 = 25

Careful!

25 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 25 m ✗

3 Add the areas

All the parts together: 300 m.

distance = 62.5 + 125 + 87.5 + 25 = 300 m

4 Check

Let's check: the average speed is 15 m/s.

That is between 0 and the top speed, 25.

So the answer makes sense!

average speed = 300 ÷ 20 ≈ 15 m/s: between 0 and 25

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer