Distance-Time Graph Walkthrough
Worksheet
Prior Knowledge:
• Calculate speed, distance or time using a formula or formula triangle.
• Calculate the gradient of a straight line.
Example 1
The diagram shows a distance-time graph for a car journey and its return home.
80
C D
60
Distance (km)
40
B
20
A E
0 1 2 3 4 5
Time (hours)
a. Which part of the journey was the fastest?
To find the fastest part of the journey, you need to look for the steepest slope (gradient).
In the diagram, we can see that the section of the journey between parts B and C has the
steepest gradient and therefore is the fastest part of the journey.
80
C D
60
Distance (km)
40
B
20
A E
0 1 2 3 4 5
Time (hours)
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Distance-Time Graph Walkthrough Worksheet
b. For how long was the car parked
80
during the journey?
C D
To find when a person or object is
stationary, look for a horizontal line. 60
Distance (km)
This means that the distance has not
changed but time has continued to 40
pass. Section C to D shows that the B
car is parked.
20
To calculate how long, subtract the A E
time that the journey restarts from 0 1 2 3 4 5
the time it stopped. Time (hours)
In this example, 2.5 – 1.5 = 1 hour.
The car was parked for 1 hour.
c. Calculate the speed for the first hour of the journey.
Section A to B covers the first hour of the journey. To calculate the speed, we can use the
formula triangle.
We already know the time is 1 hour. The distance can be found by
subtracting the distance at the start of the section (in this case, 0)
D from the distance at the end of the section (in this case, 30).
Distance
30 – 0 = 30 kilometres
S T Speed = 30
1
Speed Time
Speed = 30km/h
The gradient of the line on a distance-time graph will tell you the speed at that point. The
steeper the graph, the faster the speed.
Remember, the formulae we can use to find the gradient of a straight line are:
y −y rise
Gradient = x2 − x 1 or
2 1 run
Make sure you check the units!
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Distance-Time Graph Walkthrough Worksheet
Example 2
The diagram shows a distance-time graph for a motorbike. Find the speed of the motorbike,
giving your answer in kilometres per hour.
50
40
45
45 minutes = 60
Distance (km)
30 = 0.75 hours
20 50 − 0
Speed = 0.75 − 0 = 66.7km/h
10
0 10 20 30 40 50
Time (minutes)
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Distance-Time Graph Walkthrough Worksheet
Your Turn
1. The diagram shows a distance-time graph for a motorbike. Find the speed of the
motorbike when it was moving, giving your answer in km/h.
50
40
Distance (km)
30
20
10
0 10 20 30 40 50
Time (minutes)
2. The diagram shows a distance-time graph for a motorbike. Find the speed of the
motorbike during the fastest section of travel, giving your answer in km/h.
50
40
Distance (km)
30
20
10
0 10 20 30 40 50
Time (minutes)
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Distance-Time Graph Walkthrough Worksheet
3. The diagram shows a distance-time graph for a motorbike. Find the speed of the
motorbike during the fastest section of travel, giving your answer in km/h.
50
40
Distance (km)
30
20
10
0 10 20 30 40 50
Time (minutes)
4. The diagram shows a distance-time graph for a motorbike. Work out the average speed
of the motorbike during:
a. Section A
50
40
B
Distance (km)
30
b. Section B
20
A
10
c. The entire journey
0 10 20 30 40 50
Time (minutes)
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Distance-Time Graph Walkthrough Worksheet
5. The graph shows the journey of a cyclist. He leaves his starting position heading east.
90
E
80
70
Distance from home (m)
60
50
C D
40
B
30
20
10
A F
0 5 10 15 20 25 30
Time (s)
a. How far has the cyclist travelled f. Between which two points is the cyclist
between points A and B? traveling the fastest?
b. How far did the cyclist travel g. Between which two points is the cyclist
throughout his entire journey? traveling the slowest?
c. Describe what is happening to the h. Calculate the average speed of the
cyclist’s speed between points C and D. cyclist between points A and E.
d. Describe what is happening to the i. Calculate the average speed of the
cyclist’s speed between points C and D. cyclist between points E and F.
e. Describe what is happening to the j. Calculate the average speed through
cyclist’s speed between points B and C. the cyclist’s entire journey.
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Distance-Time Graph Walkthrough Worksheet
6. The graph shows the journey of a woman setting off from home and taking the bus into
town.
3000
G
2500 F
Distance from home (m)
2000
D E
1500
1000
500 B C
A
0 120 240 360 480 600 720 840
Time (s)
a. For the first part of her journey (A-B), f. How fast does the woman walk to the
she walks to the bus stop. How long bus stop?
does this take?
g. What is the average speed of the bus
b. How long did she wait for the bus to during the journey?
arrive?
h. Suggest what is happening between
c. How long does the journey on the bus points D and E.
(C-G) take?
i. The next day, there are no buses. The
d. How far from the woman’s house is woman sets off walking from home
the bus stop? with the same initial speed. Assuming
she walks at the same constant
speed, how long does it take her to
walk to town?
e. How far from the woman’s house is
the town?
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