Speed-time graph: (0, 0) (2, 10) (8, 10) (10, 0), find the distance

Step by step

The question

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

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.

Under part A: a triangle.

Half of 2 times 10 is 10.

Under part B: a rectangle, 6 across and 10 up.

6 times 10 is 60.

Under part C: a triangle.

Half of 2 times 10 is 10.

Careful!

10 is the top speed, read off the graph.

The distance is the area under it.

3 Add the areas

All the parts together: 80 m.

4 Check

Let's check: the average speed is 8 m/s.

That is between 0 and the top speed, 10.

So the answer makes sense!

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.