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Compound Units

Compound Units

Compound Units are measurements that require two different types of unit: speed is a compound unit as it is defined using both distance and time. Acceleration (distance and time), density (mass and volume) and pressure (force and area) are also compound units, as they require more than a single measurement to describe a quantity.

The table below shows some simple compound measurements. Compound measurements can be shown in different ways: a speed of 5 metres per second can be shown as 5ms-1 or 5m/s. In both instances, it means the same: a distance of 5 metres is covered in each second.

Measurement Meaning Units Example
Speed or Velocity Distance covered in Time kph m/s 5kph
Rates of Pay Amount per Hour £/hr £7.80/hr
Prices Price per unit £/kg 38p/kg

Example 1

A train covers 128 miles in 2 hours 30 minutes. What is the average speed of the train?

2 hours 30 minutes is 2.5 hours.

The speed of the train is distance ÷ time = 128 ÷ 2.5 = 51.2 mph

Answer: 51.2 mph

Example 2

Convert 45kph to ms-1.

45 kph-1 can be written as `frac(text(45 km))(text(1 hr))`.

Convert 45km to m, and hours to seconds:

`frac(45 times 1000)(1 times 60 times 60) = frac(45000)(3600) = 12.5ms^-1`

Answer: 12.5ms-1