Worked examples
The question
Question: the distance-time graph joins (0, 0) (2, 60) (3, 60) (5, 0), find the speed of each part.
distance-time graph: (0, 0) (2, 60) (3, 60) (5, 0)
1 Read the graph
Across: the time in hours.
Up: how far from the start, in km.
Going up: moving away from the start.
Flat: stopped.
Going down: coming back.
2 Speed of each part
Speed is the distance divided by the time.
On the graph that is the slope: up over across.
speed = distancetime = slope
Part A: 60 km in 2 h.
60 divided by 2 is 30 km/h.
A: speed = 602 = 30 km/h
Part B is flat.
The distance does not change: 0 km in 1 h.
The speed is 0: stopped.
B: speed = 01 = 0 km/h
Careful!
The flat part is high on the graph, but height is distance, not speed.
Flat means stopped.
Careful: not speed = 60 km/h ✗
Part C: 60 km in 2 h, coming back.
60 divided by 2 is 30 km/h.
C: speed = 602 = 30 km/h
3 Check
Let's check: speed times time gives back each distance: 60 and 60.
So it is right!
30 × 2 = 60, 30 × 2 = 60
Let's look back.
First: read the graph.
Then: speed of each part.
Last: check.
Answer C: speed = 602 = 30 km/h
▶ Watch it solved
The question
Question: the distance-time graph joins (0, 0) (2, 60) (3, 60) (5, 0), find the average speed.
distance-time graph: (0, 0) (2, 60) (3, 60) (5, 0)
1 Read the graph
Across: the time in hours.
Up: how far from the start, in km.
Going up: moving away from the start.
Flat: stopped.
Going down: coming back.
2 Total distance and time
Add up how far it went in each part, going and coming back: 120 km.
Flat parts add nothing.
total distance = 60 + 60 = 120 km
The whole trip took 5 h, stops too.
total time = 5 h
Careful!
The time when it stopped is part of the trip.
It goes in the total time.
Careful: the stops count in the time
3 Average speed
Average speed is the total distance divided by the total time: 24 km/h.
average speed = 1205 = 24 km/h
4 Check
Let's check: 24 times 5 gives back the total distance, 120.
So it is right!
24 × 5 = 120
Let's look back.
First: read the graph.
Then: total distance and time.
Then: average speed.
Last: check.
Answer average speed = 1205 = 24 km/h
▶ Watch it solved
The question
Question: the distance-time graph joins (0, 0) (1, 40) (2, 40) (3, 70) (5, 0), find the speed of each part.
distance-time graph: (0, 0) (1, 40) (2, 40) (3, 70) (5, 0)
1 Read the graph
Across: the time in hours.
Up: how far from the start, in km.
Going up: moving away from the start.
Flat: stopped.
Going down: coming back.
2 Speed of each part
Speed is the distance divided by the time.
On the graph that is the slope: up over across.
speed = distancetime = slope
Part A: 40 km in 1 h.
40 divided by 1 is 40 km/h.
A: speed = 401 = 40 km/h
Part B is flat.
The distance does not change: 0 km in 1 h.
The speed is 0: stopped.
B: speed = 01 = 0 km/h
Careful!
The flat part is high on the graph, but height is distance, not speed.
Flat means stopped.
Careful: not speed = 40 km/h ✗
Part C: 30 km in 1 h.
30 divided by 1 is 30 km/h.
C: speed = 301 = 30 km/h
Part D: 70 km in 2 h, coming back.
70 divided by 2 is 35 km/h.
D: speed = 702 = 35 km/h
3 Check
Let's check: speed times time gives back each distance: 40 and 30 and 70.
So it is right!
40 × 1 = 40, 30 × 1 = 30, 35 × 2 = 70
Let's look back.
First: read the graph.
Then: speed of each part.
Last: check.
Answer D: speed = 702 = 35 km/h
▶ Watch it solved
