Compound measures

A compound measure combines two units, such as km per hour.

Speed = distance ÷ time (learn this)

The formula triangle has distance at the top and speed and time at the bottom. Cover the one you want: what's left shows how to work it out (distance = speed × time; time = distance ÷ speed).

Example: a car travels 150 km in 2 hours 30 minutes. Find its average speed.

1. Time in hours: 2 hours 30 minutes = 2.5 hours
2. Speed = 150 ÷ 2.5 = 60 km/h

Example: how long does it take to travel 45 km at 60 km/h?

1. Time = 45 ÷ 60 = 0.75 hours
2. 0.75 × 60 = 45 minutes

To change km/h to m/s, change kilometres to metres (× 1000) and hours to seconds (÷ 3600).

1. Multiply by 1000 to get metres per hour.
2. Divide by 3600 to get metres per second.
3. To go back from m/s to km/h, do the opposite: × 3600, then ÷ 1000.

Example: change 72 km/h to m/s.

1. 72 × 1000 = 72 000 m in an hour
2. 72 000 ÷ 3600 = 20 m/s

Example: change 15 m/s to km/h.

1. 15 × 3600 = 54 000 m in an hour
2. 54 000 ÷ 1000 = 54 km/h

Density = mass ÷ volume (learn this)

Density is usually in g/cm³ or kg/m³. The formula triangle has mass at the top and density and volume at the bottom.

Example: a metal block has a mass of 540 g and a volume of 200 cm³. Find its density.

1. Density = 540 ÷ 200
2. 2.7 g/cm³

Example: copper has a density of 8.9 g/cm³. Find the mass of 50 cm³ of copper.

1. Mass = density × volume
2. 8.9 × 50 = 445 g

Pressure = force ÷ area (learn this)

Force is in newtons (N), area in m² (or cm²), and pressure in N/m² (or N/cm²). The formula triangle has force at the top and pressure and area at the bottom.

Example: a force of 600 N acts on an area of 0.25 m². Find the pressure.

1. Pressure = 600 ÷ 0.25
2. 2400 N/m²

Example: a box exerts a force of 1200 N and a pressure of 300 N/m². What area is it standing on?

1. Area = force ÷ pressure
2. 1200 ÷ 300 = 4 m²

The same force on a smaller area gives a bigger pressure.