GCSE(F),

**Compound Units** are units that require two different types of measurement: speed is a compound unit as it is defined with bothe distance and time. Acceleration, density and pressure 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 cover in Time | kph m/s | 5kph |

Rates of Pay | Amount per Hour | £/hr | £7.80/hr |

Prices | Price per unit | £/kg | 38p/kg |

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

Answer: 51.2 mph

2 hours 30 minutes is 2.5 hours.

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

2. Convert 45kph to ms^{-1}.

Answer: 12.5ms^{-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`

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