1. October 4, 2012
Compound measures
1. Speed, density and population density.
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2. Explanation October 4, 2012
Some things in the physical world, we measure in simple
units.
For example:
Length can be measured in centimetres,
or metres, or kilometres.
Time can be measured in seconds, or
minutes, or hours.
Mass can be measured in grams, or
kilograms, or tonnes.
But how do we measure speed?
Speed is the amount of distance travelled in an amount
of time.
This makes it a compound measure.
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3. Explanation October 4, 2012
Speed is a compound measure, because it is calculated
from two other measurements, distance and time.
total distance travelled
average speed =
total time taken
The units of your answer will depend on the units of the
question.
An athlete runs 100 metres in 20 seconds.
100 m
average speed = = 0.5 m/s
20 s
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4. Explanation October 4, 2012
Sometimes it is the convention to write a compound
measure using particular units.
A delivery driver travels 45 kilometres in 30 minutes.
45 km
average speed = = 1.5 km/minute
30 minutes
But we would tend to write the speed of a vehicle in
kilometres per hour.
To get an answer in these units, first change the time to
hours.
45 km
average speed = = 1.5 km/h
0.5 hours
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5. Explanation October 4, 2012
Instead of writing
total distance travelled
average speed =
total time taken
d
You can simplify this to s=
t
Any formula that takes this form can be rearranged
using a useful triangle: d
t=
Cover the value d s
you are trying to d
find. s× t s=
t
d = s×t
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6. Explanation October 4, 2012
Density is the mass of something, divided by the space it
fills. so
density =
mass
volume
or m
d×v
The units we tend to describe mass in are:
grams per cubic centimetre g/cm³
kilograms per cubic metre kg/cm³
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7. Examples October 4, 2012
Calculate the density of a piece of metal that has a mass
of 2000 kg and a volume of 0.5 m³.
m 2000 kg 4000 kg
d= d= d= d = 4000 kg/m³
v 0.5 m³ 1m³
The density of gold is 9.3 g/cm³. Calculate the mass of
a gold bar with a volume of 30 cm³
m=d×v
m = 9.3 g/cm³ × 30 cm³ m
m = 279 g d×v
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8. Explanation October 4, 2012
Population density means the average number of people
in a place, that live in a specific unit of area.
This is usually written as population per square mile, or
square kilometre.
total population
pd =
area
1 km
p
pd = so
a
p
1 km
pd × a
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9. Examples October 4, 2012
An island has a population of 18,000 people. The area of
the island is 6 square kilometres. Calculate the
population density.
p 18,000 people
pd = pd = pd = 3,000/km²
a 6 km²
What is the area of a city with a population of 1.2 million
and a population density of 8,000/km² ?
p 1.2 million
a=
pd
a=
8,000
a = 150 km² p
pd × a
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