Compound units: speed, density, pressure
A compound unit combines two basic measures using ratio. The three you absolutely must know for GCSE are speed, density and pressure, all famous "formula triangles".
Speed
Speed = distance / time. Unit symbol: m/s, km/h, mph.
| Find | Formula | |
|---|---|---|
| Speed | average rate | s = d / t |
| Distance | how far | d = s × t |
| Time | how long | t = d / s |
Worked example: a cyclist covers 36 km in 1.5 hours. Speed = 36 / 1.5 = 24 km/h.
Density
Density = mass / volume. Unit symbols: g/cm³, kg/m³.
| Find | Formula |
|---|---|
| Density | ρ = m / V |
| Mass | m = ρ × V |
| Volume | V = m / ρ |
Worked example: a metal cube has mass 540 g and volume 60 cm³. Density = 540 / 60 = 9 g/cm³.
Pressure
Pressure = force / area. Unit symbols: N/m² (= Pascal, Pa), N/cm².
| Find | Formula |
|---|---|
| Pressure | P = F / A |
| Force | F = P × A |
| Area | A = F / P |
Worked example: a 600 N force is applied over 0.2 m². Pressure = 600/0.2 = 3000 Pa.
Reading the formula triangle
Cover the variable you want; the position of the others tells you whether to multiply or divide. (For speed: D on top, S × T on the bottom.)
Mixed unit problems
Watch for unit mismatches.
Worked example: a car travels 60 km in 45 minutes. Find the speed in km/h.
- 45 min = 0.75 h.
- 60 / 0.75 = 80 km/h.
Linking to compound unit conversions (R1)
Worked example: density 1.2 g/cm³ — express in kg/m³.
- × 1000 → 1200 kg/m³.
⚠Common mistakes
- Time in mixed units — 1 h 20 min = 80 min OR 4/3 h, NOT 1.20 h.
- Density × volume confusion — m = ρ × V, NOT m = V/ρ.
- Pressure with mismatched units — P (N/m²) needs A in m², not cm².
- Average speed myth — average ≠ (s1 + s2)/2 unless equal time. Use TOTAL distance / TOTAL time.
- Forgetting to convert km ↔ m or g ↔ kg before applying the formula.
➜Try this— Quick check
A pressure of 12 N/cm² acts on 50 cm². Find the force.
- F = P × A = 12 × 50 = 600 N.
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