Compound Measures: Speed, Density, Pressure
Compound Measures: Speed, Density, Pressure
Compound measures combine two different units. The three you must know are speed, density and pressure.
Speed
Speed = distance ÷ time
Distance = speed × time
Time = distance ÷ speed
Remember the triangle: D on top, S and T on the bottom. Cover the one you want.
Units must be consistent: if speed is in km/h, distance must be in km and time in hours.
Worked Example: A car travels 150 miles in 2 hours 30 minutes. Find its average speed.
- Time = 2.5 hours (convert 30 min = 0.5 hours)
- Speed = 150 ÷ 2.5 = 60 mph
Worked Example: A train travels at 90 km/h for 40 minutes. How far does it go?
- Time = 40/60 = 2/3 hours
- Distance = 90 × 2/3 = 60 km
Density
Density = mass ÷ volume
Mass = density × volume
Volume = mass ÷ density
Density measures how much mass is packed into a given volume. Common units: g/cm³ or kg/m³.
Worked Example: A block of metal has a mass of 540g and a volume of 200 cm³. Find its density.
- Density = 540 ÷ 200 = 2.7 g/cm³
Worked Example: A liquid has density 0.8 g/cm³. What is the mass of 250 cm³ of the liquid?
- Mass = 0.8 × 250 = 200g
Pressure
Pressure = force ÷ area
Force = pressure × area
Area = force ÷ pressure
Pressure is measured in Pascals (Pa) or N/m². 1 Pa = 1 N/m².
Worked Example: A box weighing 360 N stands on the floor. Its base measures 0.3 m by 0.4 m. Find the pressure on the floor.
- Area = 0.3 × 0.4 = 0.12 m²
- Pressure = 360 ÷ 0.12 = 3000 Pa (or 3000 N/m²)
Converting Units
| Conversion | Factor |
|---|---|
| km/h → m/s | ÷ 3.6 (or × 1000 ÷ 3600) |
| m/s → km/h | × 3.6 |
| g/cm³ → kg/m³ | × 1000 |
| kg/m³ → g/cm³ | ÷ 1000 |
Worked Example: Convert 72 km/h to m/s.
- 72 ÷ 3.6 = 20 m/s
Distance-Time Graphs
- The gradient of a distance-time graph gives the speed
- A horizontal line means stationary (speed = 0)
- A steeper line means faster speed
- A curved section means acceleration (changing speed)
Velocity-Time Graphs
- The gradient gives the acceleration
- The area under the graph gives the distance travelled
- A horizontal line means constant speed
- A line going down means deceleration
Worked Example: A velocity-time graph shows a straight line from (0, 0) to (10, 20) then horizontal to (25, 20).
- Acceleration for first 10 seconds = 20/10 = 2 m/s²
- Distance = area of triangle + area of rectangle
- = ½ × 10 × 20 + 15 × 20 = 100 + 300 = 400 m
Exam Tips
- Learn the formula triangles — they help you rearrange quickly under exam pressure
- Always convert units before calculating (e.g. minutes to hours for speed)
- In velocity-time graphs, the area represents distance even when the shape is a triangle or trapezium — use the appropriate area formula
- Density questions often combine with volume formulas (e.g. find the mass of a sphere given density and radius)