Step by step
The question
Question: the speed-time graph joins (0, 0) (5, 20) (10, 20), find the distance.
speed-time graph: (0, 0) (5, 20) (10, 20)
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 20 is 50.
A: area = ½ × 5 × 20 = 50
Under part B: a rectangle, 5 across and 20 up.
5 times 20 is 100.
B: area = 5 × 20 = 100
Careful!
20 is the top speed, read off the graph.
The distance is the area under it.
Careful: not distance = 20 m ✗
3 Add the areas
All the parts together: 150 m.
distance = 50 + 100 = 150 m
4 Check
Let's check: the average speed is 15 m/s.
That is between 0 and the top speed, 20.
So the answer makes sense!
average speed = 150 ÷ 10 ≈ 15 m/s: between 0 and 20
Let's look back.
First: read the graph.
Then: distance = area.
Then: add the areas.
Last: check.
Answer
distance = 50 + 100 = 150 m