Compound Units
A compound unit combines two or more standard units — like distance and time to create speed. Understanding how to work with them is essential for solving real-world problems in science, engineering, and your GCSE Maths exam.
Key Compound Units and Their Formulas
The three most common compound units are Speed, Density, and Pressure. You must convert all measurements to consistent units before calculating. Use these formula triangles to rearrange each formula.
Speed
Speed = Distance ÷ Time
Density
Density = Mass ÷ Volume
Pressure
Pressure = Force ÷ Area
Key Unit Conversions
You must use consistent units before you calculate. The trickiest conversions are for area and volume.
Area Conversions
When converting length units, square the conversion factor for area.
Since $1 \text{ m} = 100 \text{ cm}$:
Volume Conversions
For volume, cube the conversion factor.
Since $1 \text{ m} = 100 \text{ cm}$:
Worked Examples
Example 1: Speed Calculation
A car travels 18 km in 15 minutes. Calculate its speed in m/s.
- Convert units:
Distance: $18 \text{ km} = 18{,}000 \text{ m}$.
Time: $15 \text{ min} = 900 \text{ s}$. - Apply formula: Speed $=$ Distance $\div$ Time.
- Calculate: Speed $= 18{,}000 \div 900 = \mathbf{20 \text{ m/s}}$.
Example 2: Density Calculation
A block has a mass of 4.5 kg and a volume of 500 cm³. Calculate its density in g/cm³.
- Convert units:
Mass: $4.5 \text{ kg} = 4{,}500 \text{ g}$.
Volume is already in cm³. - Apply formula: Density $=$ Mass $\div$ Volume.
- Calculate: Density $= 4{,}500 \div 500 = \mathbf{9 \text{ g/cm}^3}$.
Tutor Insights
🤔 Common Misunderstandings
- Area/volume conversions: Forgetting to square or cube the conversion factor. If the unit is squared, so is the factor.
- Time conversions: Confusing decimal hours with minutes. 0.5 hours = 30 minutes, not 50.
📝 Common Exam Mistakes
- Calculating with inconsistent units. Convert all measurements first — always.
- Missing units in the final answer. A number without units is an incomplete answer.
- Mixing up the formulas. The formula triangles prevent this — cover the quantity you want and the remaining two show you whether to multiply or divide.
Practice Questions
- A snail crawls 30 cm in 2 minutes. What is its speed in cm/min?
- A brick has a mass of 2.4 kg and a volume of 1200 cm³. What is its density in g/cm³?
- A cyclist travels at an average speed of 18 km/h for 2.5 hours. How far do they travel?
- Convert 54 km/h to m/s.
Show Answers
- Speed $= 30 \div 2 = \mathbf{15 \text{ cm/min}}$.
- Mass $= 2.4 \text{ kg} = 2{,}400 \text{ g}$. Density $= 2{,}400 \div 1{,}200 = \mathbf{2 \text{ g/cm}^3}$.
- Distance $= 18 \times 2.5 = \mathbf{45 \text{ km}}$.
- $54 \text{ km} = 54{,}000 \text{ m}$. 1 hour $= 3{,}600$ s. Speed $= 54{,}000 \div 3{,}600 = \mathbf{15 \text{ m/s}}$.
Need Help with Compound Units?
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