Step by step
The question
Question: the speed-time graph joins (0, 0) (6, 18) (8, 18), find the distance.
speed-time graph: (0, 0) (6, 18) (8, 18)
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 6 times 18 is 54.
A: area = ½ × 6 × 18 = 54
Under part B: a rectangle, 2 across and 18 up.
2 times 18 is 36.
B: area = 2 × 18 = 36
Careful!
18 is the top speed, read off the graph.
The distance is the area under it.
Careful: not distance = 18 m ✗
3 Add the areas
All the parts together: 90 m.
distance = 54 + 36 = 90 m
4 Check
Let's check: the average speed is 11.3 m/s.
That is between 0 and the top speed, 18.
So the answer makes sense!
average speed = 90 ÷ 8 ≈ 11.3 m/s: between 0 and 18
Let's look back.
First: read the graph.
Then: distance = area.
Then: add the areas.
Last: check.
Answer
distance = 54 + 36 = 90 m