April 13, 2023

1. Speed, density and population density.

Compound measures

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April 13, 2023

Some things in the physical world, we measure in simple units.

Length can be measured in centimetres, or metres, or kilometres.

For example:

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.

Explanation

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April 13, 2023

Speed is a compound measure, because it is calculated from two other measurements, distance and time.

The units of your answer will depend on the units of the question.

average speed =total distance travelled

total time taken

average speed =100 m

20 s= 0.5 m/s

Explanation

An athlete runs 100 metres in 20 seconds.

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April 13, 2023

Sometimes it is the convention to write a compound measure using particular units.

A delivery driver travels 45 kilometres in 30 minutes.

average speed =45 km

30 minutes= 1.5 km/minute

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.

average speed =45 km

0.5 hours= 1.5 km/h

Explanation

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April 13, 2023

average speed =total distance travelled

total time taken

Instead of writing

You can simplify this to

s td× s =

td

t = sd

d = s × t

Any formula that takes this form can be rearranged using a useful triangle:

Cover the value you are trying to find.

s =td

Explanation

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April 13, 2023

Density is the mass of something, divided by the space it fills. so

density =mass

volumeor

d vm×

The units we tend to describe mass in are:

grams per cubic centimetre g/cm³

kilograms per cubic metre kg/cm³

Explanation

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April 13, 2023

Calculate the density of a piece of metal that has a mass of 2000 kg and a volume of 0.5 m³.

The density of gold is 9.3 g/cm³. Calculate the mass of a gold bar with a volume of 30 cm³

d =vm

d =0.5 m³

2000 kgd = d = 4000 kg/m³

1m³

4000 kg

d vm×

m = d × v

m = 9.3 g/cm³ 30 cm³

m = 279 g

×

Examples

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April 13, 2023

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.

1 km

1 km

pd =total population

area

pd =p

a

pd ap×

so

Explanation

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April 13, 2023

An island has a population of 18,000 people. The area of the island is 6 square kilometres. Calculate the population density.

pd ap×

pd =p

a18,000 people

6 km²pd = pd = 3,000/km²

What is the area of a city with a population of 1.2 million and a population density of 8,000/km² ?

pd

pa =

1.2 million

8,000a = a = 150 km²

Examples

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