Speed-time graph: (0, 0) (5, 30) (10, 30) (15, 0), find the distance

Step by step, with the reason for every step · Speed-time graphs · Algebra 1

Step by step

The question

Question: the speed-time graph joins (0, 0) (5, 30) (10, 30) (15, 0), find the distance.

speed-time graph: (0, 0) (5, 30) (10, 30) (15, 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 30 is 75.

A: area = ½ × 5 × 30 = 75

Under part B: a rectangle, 5 across and 30 up.

5 times 30 is 150.

B: area = 5 × 30 = 150

Under part C: a triangle.

Half of 5 times 30 is 75.

C: area = ½ × 5 × 30 = 75

Careful!

30 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 30 m ✗

3 Add the areas

All the parts together: 300 m.

distance = 75 + 150 + 75 = 300 m

4 Check

Let's check: the average speed is 20 m/s.

That is between 0 and the top speed, 30.

So the answer makes sense!

average speed = 300 ÷ 15 ≈ 20 m/s: between 0 and 30

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer

distance = 75 + 150 + 75 = 300 m

Your turn

Try this one yourself, then check:

speed-time graph: (0, 0) (5, 45) (10, 45) (15, 0)

Show the answer

distance = 450 m

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