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

Step by step

The question

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

speed-time graph: (0, 0) (5, 10) (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 10 is 25.

A: area = ½ × 5 × 10 = 25

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

10 times 10 is 100.

B: area = 10 × 10 = 100

Under part C: a triangle.

Half of 5 times 10 is 25.

C: area = ½ × 5 × 10 = 25

Careful!

10 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 10 m ✗

3 Add the areas

All the parts together: 150 m.

distance = 25 + 100 + 25 = 150 m

4 Check

Let's check: the average speed is 7.5 m/s.

That is between 0 and the top speed, 10.

So the answer makes sense!

average speed = 150 ÷ 20 ≈ 7.5 m/s: between 0 and 10

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer