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© Nuffield Foundation 2011© Nuffield Foundation 2011
Nuffield Free-Standing Mathematics Activity
Road test
© Brett Wilson
© Nuffield Foundation 2011© Nuffield Foundation 2011
In this activity you will use data from a speed test to draw and interpret graphs.
© Brett Wilson
© Nuffield Foundation 2011© Nuffield Foundation 2011
Drivers have always been interested in how fast cars go – and how quickly they stop!
Graphs provide a useful illustration of the data.
© Nuffield Foundation 2011© Nuffield Foundation 2011
Think about…What comments can you make?Why do you think the true and indicated speeds are different?
Here are some data from a speed test.Acceleration from rest
Time True Speed Indicated Speed
t (seconds) v (miles per hour) u (miles per hour)
2.3 30 34
3.5 40 45
5.5 50 55
6.8 60 66
9.4 70 78
13.1 80 89
20.5 90 99
© Nuffield Foundation 2011© Nuffield Foundation 2011
The brakes were also tested by measuring the distance travelled by the car in coming to rest from different speeds. The track surface was dry and maximum braking was used.
Why are only dry surfaces used for the tests?
How might the results be different if wet road tests were included?
Brakes
True speed Distance
v (miles per hour) d (metres)
30 9.5
50 27.5
70 52.4
85 98.7
© Nuffield Foundation 2011© Nuffield Foundation 2011
Sports car accelerating
0
20
40
60
80
100
0 20 40 60 80 100
Indi
cate
d sp
eed
(mph
)
True speed (mph)
Graph of indicated speed against true speed
Series1
© Nuffield Foundation 2011© Nuffield Foundation 2011
Sports car accelerating
0
20
40
60
80
100
0 5 10 15 20 25
True
spee
d (m
ph)
Time (s)
Graph of true speed against time
True Speed (miles per hour)
© Nuffield Foundation 2011© Nuffield Foundation 2011
Sports car accelerating
0
20
40
60
80
100
0 5 10 15 20 25
Indi
cate
d sp
eed
(mph
)
Time (s)
Graph of indicated speed against time
© Nuffield Foundation 2011© Nuffield Foundation 2011
Sports car braking
0
20
40
60
80
100
0 20 40 60 80 100
Dis
tanc
e (m
etre
s)
Speed (mph)
Graph of distance against speed
© Nuffield Foundation 2011© Nuffield Foundation 2011
Reflect on your work
What does each graph tell you about the car’s performance during the test drive?
Road test