Compound Measures
Speed, density and pressure, and other rates - converting units and rearranging the formulae.
Watch the lesson
Every point below, worked through in one video, and each point links straight to its own part.
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.
Common mistakes in Compound Measures
The slips that cost marks year after year, and what to do instead.
Treating minutes as decimals of an hour, so 20 minutes becomes 0.2 hours.
Divide minutes by 60: 20 minutes is = of an hour, and 1 hour 30 minutes is 1.5 hours.
Multiplying when you should divide after rearranging, as in time = speed × distance.
Start from speed = distance ÷ time and rearrange it: time = distance ÷ speed. So 150 miles at 60 mph takes 150 ÷ 60 = 2.5 hours.
Converting m/s to km/h in one step, such as multiplying by 60 or by 1000.
Change one unit at a time: 20 m/s is 20 × 3600 = 72 000 m in an hour, which is 72 km/h. Multiplying by 3.6 does both steps at once.
Finding an average speed by averaging the speeds of each part of the journey.
Use total distance ÷ total time. 60 km at 30 km/h takes 2 hours and 60 km at 60 km/h takes 1 hour, so the average is 120 ÷ 3 = 40 km/h, not 45.
Reading distance from the gradient of a velocity–time graph, or taking a flat section to mean stopped.Higher only
On a velocity–time graph the area underneath is the distance and the gradient is the acceleration. A flat section means a steady speed.
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.
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.
Ready to practise Compound Measures?
Sign up free to practise this topic - questions that adapt to how you're doing, with instant encouraging feedback on every answer. No card needed.
Already have an account? Log in