version

Teacher
Car Speedometers
How can you convert from mph to
kph so that you can mark a car's
speedometer in both units?
Contents
Initial Problem Statement 2
Narrative 3-4
Solutions 5-7
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Car
Speedometers
Appendix 8
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Teacher
Car Speedometers
The speed indicator in UK cars tells drivers how
fast they are going in the Imperial unit miles per
hour (mph), as this is the unit of speed used to
indicate speed limits on UK roads. However, if
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you drive elsewhere in Europe speed limits are
given in the metric unit of kilometres per hour
(kph).
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How can you convert
from mph to kph so that
you can mark a car's
speedometer in both
units?
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Initial Problem Statement
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Car speedometers
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Figure 1.
Discussion
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Car Speedometers
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What relationships do you need to know to convert from mph to kph?
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The following table shows some different units and the conversion between them.
Unit 1
Equivalent unit 2
1760 yards
3 feet
1 foot
12 inches
1 inch
2.54 cm
1m
100 cm
1 km
1000 cm
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1 mile
1 yard
Discussion
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Which of the above conversions relates an Imperial measurement to a metric
measurement?
Activity 1
Use the information in the above table to find a conversion from miles per hour to
kilometres per hour.
Activity 2
Use your relationship to convert the following common European speed limits in
kph to equivalent speeds in mph. Give your results to the nearest whole value and
compare your results with the above picture of a speedometer.
European speed (kph)
UK speed (mph)
50
80
100
120
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Teacher
A typical speedometer from a UK car is shown on the centre dial below. The outer numbers show
speed in mph while the inner ones show speed in kph.
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Narrative
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Teacher
Activity 3
How would you convert mph to metres per second (ms-1)?
Discussion
Where else might unit
conversion be important?
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Car Speedometers
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How many metres do you
travel each second when
travelling on a motorway at
70 mph?
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Discussion
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Teacher
Solutions
Discussion solution
To convert from mph to kph you need to know the relationship between miles
and kilometres. As both units measure a distance per hour you do not need any
time relationships. This means that if you find a conversion between miles and
kilometres you will automatically find a relationship between miles per hour and
kilometres per hour.
In the table below shows several units conversion equivalent values.
Equivalent unit 2
1760 yeards
1 yard
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Unit 1
1 mile
3 feet
1 foot
12 inches
1 inch
2.54 cm
1m
100 cm
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Discussion solution
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The first three rows convert from one Imperial unit to another. The fourth
conversion relates an Imperial unit (the inch) to a metric unit (the cm). The last two
rows convert one metric unit to another.
Activity 1 solution
To convert from mph to kph you need to find the conversion between miles and
kilometres. The first row in the above table gives a starting point for this.
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1 mile = 1760 yards.
Now use the second row to express a mile in feet.
1 yard = 3 feet so 1760 yards = 1760 × 3 = 5280 feet
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Continuing
1 foot = 12 inches so 5280 feet = 5280 × 12 = 63360 inches
1 inch = 2.54 cm so 63360 inches = 63360 × 2.54 = 160934.4 cm
Now you need to convert cm to kilometres.
The table states that 1 m is equivalent to 100 cm. To find the conversion from cm to
m you simply divide both sides by 100 so that
1 m = 100 cm
1 m 100 cm
=
100
100
0.01 m = 1 cm
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1000 m
Car Speedometers
1 km
Teacher
Using this
1 cm = 0.01 m so 160934.4 cm = 160934.4 × 0.01 = 1609.344 m
Similarly converting metre to kilometres
1 m = 0.001 km so 1609.344 m = 1609.344 × 0.001 = 1.609344 km
You have now found your conversion: 1 mile = 1.609344 km.
As the speed you are converting is mph to kph then it follows that
1 mph = 1.609344 kph
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1 mph
1.609344 kph
=
1.609344
1.609344
Activity 2 solution
Car Speedometers
0.621… mph = 1 kph
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Using the above conversion gives the following equivalent speeds in mph for
common European speed limits (to the nearest whole value).
European speed (kph)
UK speed (mph)
50
31
50
62
120
75
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80
100
Activity 3 solution
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To convert mph to metres per second you need to change both the distance units
and the time units. The above has already converted the distance units to give
1 mph = 1.609344 kph =1609.344 metres per hour (as 1 km = 1000 m).
There are 60 minutes in 1 hour so in one minute the distance travelled is one-sixtieth
of 1609.344 metres,
1609.344 metres per hour = 26.8224 metres per minute.
Similarly there are 60 seconds in one minute so
26.8224 metres per minute = 0.44704 metres per second (ms-1)
This gives the final conversion as
1 mph = 0.44704 ms-1
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1 mph = 1.609344 kph
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To convert kph to mph you simply divide both sides by 1.609344
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If you are travelling at 70 mph on a motorway your equivalent speed in ms-1 is
70 mph = 70× 0.44704 ≈ 31 ms-1,
Teacher
Discussion solution
i.e. every second you travel about 31 metres.
Discussion solution
Many different units are used in engineering and accurate conversion between
them is important. Examples include
Car Speedometers
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Conversion of deg C to deg C
Conversion of deg C to Kelvin (K)
Conversion of metal thickness in mm to standard weight gauge (SWG)
Conversion of pressure in pounds per square inch (PSI) to kilopascal (kPa)
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Teacher
Appendix
mathematical coverage
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Car Speedometers
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Use algebra to solve engineering problems
• Be able to convert from one set of units to another
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