7.2 Compound measures: speed, density and pressure — Learn

Prerequisites: unit conversions and rearranging a formula with inverse operations.

Before you begin

You should be able to convert units and rearrange a formula by using inverse operations.

Objectives

• Calculate speed, distance and time.
• Calculate density, mass and volume.
• Calculate pressure, force and area.
• Choose units that match the quantities.

Speed

Speed tells you the distance travelled per unit of time. The formula is $\text{speed}=\text{distance}\div\text{time}$.

Example 1. A train travels $150$ km in $2.5$ hours. Find its average speed.

The average speed is $60$ km/h. Rearranging gives distance $=\text{speed}\times\text{time}$ and time $=\text{distance}\div\text{speed}$.

Example 2. A cyclist travels at $8$ m/s for $45$ seconds.

Density and pressure

Density is mass per unit volume: $\text{density}=\text{mass}\div\text{volume}$. Pressure is force per unit area: $\text{pressure}=\text{force}\div\text{area}$.

Example 3. A block has mass $540$ g and volume $200\text{ cm}^3$.

Example 4. A force of $360$ N acts on an area of $0.12\text{ m}^2$.

One pascal, written Pa, is one newton per square metre. Check that all units agree before substituting.

Watch out. A common error is to multiply distance by time when finding speed. For $150$ km in $2.5$ hours, divide: $150\div2.5=60$ km/h. Multiplying gives $375$ km hours, which is not a speed.

Progress check. A runner covers $400$ m in $80$ seconds. Which formula gives the speed, and what units will the answer use?

You should now be able to

• calculate speed, distance and time from the formula;
• calculate density, mass and volume from the formula;
• calculate pressure, force and area from the formula;
• convert units first when the quantities do not match.