Rates of change and unit conversions
Compound units
Compound units measure a quantity per another quantity. Common examples:
| Quantity | Unit | Formula |
|---|---|---|
| Speed | m/s, km/h, mph | distance ÷ time |
| Density | g/cm³, kg/m³ | mass ÷ volume |
| Pressure | N/m², Pa | force ÷ area |
| Population density | people/km² | population ÷ area |
The DST triangle
For speed-distance-time problems:
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
Same triangle pattern works for density (mass ÷ volume) and pressure (force ÷ area).
Unit consistency
The single most common source of lost marks. Before you start:
- Convert to consistent units.
- Common conversions to memorise:
| From | To | Multiply by |
|---|---|---|
| km | m | 1000 |
| m | cm | 100 |
| cm | mm | 10 |
| kg | g | 1000 |
| L | mL (or cm³) | 1000 |
| hour | minute | 60 |
| minute | second | 60 |
Converting compound units
Example: convert 72 km/h to m/s. 72 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 72 × 1000 ÷ 3600 = 20 m/s.
Quick rule for km/h → m/s: divide by 3.6.
Time
Be careful with mixed units (hours and minutes). Convert first.
Example: 2 h 15 min = 2.25 h (not 2.15 h).
Average speed for a journey
Average speed = total distance ÷ total time. Not the average of two speeds.
Example: 30 km at 60 km/h, then 30 km at 40 km/h. Time 1 = 0.5 h; Time 2 = 0.75 h. Total = 1.25 h. Average speed = 60 ÷ 1.25 = 48 km/h (not 50).
Common CCEA exam tip
When the answer is wrong by exactly a factor of 1000 or 60, it's nearly always a unit-conversion error. Always write the units beside every numerical step.
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