Compound Measures
Speed, density and pressure, and other rates - converting units and rearranging the formulae.
Learn
Compound Measures, explained point by point
Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.
Use speed = distance ÷ time, and rearrange it
Speed is distance shared over time: 150 miles in 2.5 hours is 60 mph. Rearrange for whichever is missing: distance = speed × time, time = distance ÷ speed. Times must be in the right form - 20 minutes is hour, not 0.2 hours.
Use density = mass ÷ volume
Density says how much mass is packed into each unit of volume: 540 g in 200 cm³ is 2.7 g/cm³. Rearrange the same way as speed: mass = density × volume, volume = mass ÷ density. The units in the answer follow from the units you fed in.
Use pressure = force ÷ area
Pressure spreads a force over an area: a 300 N force on 0.5 m² gives 600 N/m². The same triangle of rearrangements applies. Intuition check: the same force on a SMALLER area gives a bigger pressure - that is why drawing pins work.
Convert between compound units - m/s to km/h, g/cm³ to kg/m³
Convert one unit at a time. For 20 m/s to km/h: 20 m is 0.02 km, and 3600 seconds make an hour, so 20 × 3.6 = 72 km/h. Sense-check the direction - the number of km/h should be bigger than the number of m/s.
Read average speed from a distance–time graph
Average speed over a section is total distance ÷ total time - the gradient of the line joining the section's start and end. A stop (flat section) still counts its time, which drags the average down.
Use velocity–time graphs: gradient for acceleration, area for distanceHigher only
On a velocity–time graph the gradient is acceleration and the AREA under the graph is distance travelled. Split the area into triangles and rectangles (or trapezia) and add them up. A flat section means steady speed, not stopped - that is the distance–time trap.
Practice
Try a Compound Measures question
A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.
A car travels 90 km in 1 hour 30 minutes at a steady speed. Work out its speed in km/h.
- 135
- 45
- 6
- 60
Show the answer and the working
Answer: 60
The time must be written in hours first, so 1 hour 30 minutes becomes 1.5 hours before dividing.
- Convert the time to hours: 30 minutes = 0.5 hours, so the time is 1.5 hours.
- Use speed = distance ÷ time = 90 ÷ 1.5.
- 90 ÷ 1.5 = 60, so the speed is 60 km/h.