This document provides information about distance-time graphs, including: - Distance-time graphs plot the distance an object is from its starting point on the y-axis against time on the x-axis. - Various graphs are presented and described showing examples of journeys by car and bicycle, which can be used to calculate information like distance, time, speed and acceleration. - The slope of lines on the graphs represents speed, with steeper lines indicating faster movement. Curved lines can show changes in speed like acceleration and deceleration. - Distance-time graphs can provide data to ask questions about distance, time, speed and changes in speed for different objects and scenarios.

1. DISTANCE TIME GRAPHS

2. DISTANCE TIME GRAPHS
Time and distance graph questions
often appear on examinations. As the
name suggests, the axes are time
(usually on the X axis) and distance
(usually on the Y axis). The distance of
an object from its starting position is
plotted against the time it takes to get
there.
This is graph of a family car journey
from home for a day at the beach.
• How long did it take to get there?
• How long did they stay?
• How far away was it?
• How long did it take to get back?
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0
0 1 2 3 4 5 6 7 8 9 10
Time (hours)
Distance(km)
GRAPH OF A DRIVE TO THE BEACH

3. Look at the journey on the right. It shows a
cyclist’s journey from home to a post office and
back.
• How far away is the post office?
• How long did the journey take from home to
the post office?
• How long did the cyclist wait at the post
office?
• What do you think might be 300 metres away
from the home? Why?
• If the cyclist left at 10:35AM what time would
they get back home?
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0 1 2 3 4 5 6 7 8 9 10
Time (minutes)
Distance(m)
DISTANCE TIME GRAPHS
A CYCLE TRIP TO THE POST OFFICE

4. We can use time and distance graphs to work
out average speeds between points on lines.
Between points A and B the bike travels 300
metres in 120 seconds (2 minutes)
We can now calculate the average speed
between the two points.
300 ÷ 120 = 2.5 m/s
• What was the average speed
between C and D? Was it faster?
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0 1 2 3 4 5 6 7 8 9 10
Time (minutes)
Distance(m)
Speed =
Distance Travelled (m)
Time Taken (s)
A
B
DISTANCE TIME GRAPHS
A CYCLE TRIP TO THE POST OFFICE
C
D

5. You can also compare the speeds of different
objects by looking at their gradients (the angle of
the line)
Here are some model rocket car predictions.
Car A travels 100m in 2 seconds: 100÷2=50m/s
Car B travels 100m in 5 seconds: 100÷5=20m/s
Car C travels 100m in 10 seconds: 100÷10=10m/s
Steeper lines represent faster movement. 10
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0 1 2 3 4 5 6 7 8 9 10
Time (second)
Distance(m)
DISTANCE TIME GRAPHS
A B C

6. In reality vehicles do not always move at the
same speed and when they speed up we call
this acceleration and when they slow down we
call this deceleration.
Green is a period of acceleration – the speed
increases over time.
Red is deceleration – the speed decreases over
time.
The black line represents the line of average
speed between A and B
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0 1 2 3 4 5 6 7 8 9 10
Time (second)
Distance(m)
DISTANCE TIME GRAPHS
A
B

7. When looking at distance time graphs
some journeys may not end up back
at the destination. Sometimes the
lines may be curved and the shape of
the curve can tell us how something is
changing.
The blue line shows a fast, steady
speed but no return.
The red line show a journey with a
stop and a return
The green line shows acceleration,
then deceleration and finally a stop
some distance away
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0 1 2 3 4 5 6 7 8 9 10
Time (seconds)
Distance(m)
GRAPH SHOWING DIFFERENT TYPES OF MOVEMENT
Steady, fast
speed
Stationary
Steady return
to start
Steady
speed
Getting
faster
Getting
slower
Stationary
DISTANCE TIME GRAPHS

8. DISTANCE TIME GRAPHS
0 20 40 60 80 100 120 140
Time (seconds)
Distance(miles)
0
2
4
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BLOODHOUND SSC – PREDICTED DISTANCE TIME GRAPH
This is a distance time graph
for Bloodhound SSC.
Using your knowledge, work
in groups or teams to find
mathematical questions you
can ask using this graph.
e.g. How far does it travel?

9. RACE FOR THE LINE