Speed-time graph: (0, 0) (4, 12) (10, 12) (14, 0), find the distance Step by Step

Step by step

The question

Question: the speed-time graph joins (0, 0) (4, 12) (10, 12) (14, 0), find the distance.

speed-time graph: (0, 0) (4, 12) (10, 12) (14, 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 4 times 12 is 24.

A: area = ½ × 4 × 12 = 24

Under part B: a rectangle, 6 across and 12 up.

6 times 12 is 72.

B: area = 6 × 12 = 72

Under part C: a triangle.

Half of 4 times 12 is 24.

C: area = ½ × 4 × 12 = 24

Careful!

12 is the top speed, read off the graph.

The distance is the area under it.

Careful: not distance = 12 m ✗

3 Add the areas

All the parts together: 120 m.

distance = 24 + 72 + 24 = 120 m

4 Check

Let's check: the average speed is 8.57 m/s.

That is between 0 and the top speed, 12.

So the answer makes sense!

average speed = 120 ÷ 14 ≈ 8.57 m/s: between 0 and 12

Let's look back.

First: read the graph.

Then: distance = area.

Then: add the areas.

Last: check.

Answer