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This page sets out the method for speed, density and pressure in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Speed, density and pressure topic page.
When you have two of the three quantities and need the third, cover the one you want.
When a journey has two or more parts at different speeds and you want the average speed.
Speed = distance ÷ time. A car that travels 180 km in 3 hours has an average speed of 180 ÷ 3 = 60 km/h.
Density = mass ÷ volume. With mass in grams and volume in cm³, the density is in g/cm³.
Pressure = force ÷ area. A force of 400 N on an area of 8 m² gives a pressure of 400 ÷ 8 = 50 N/m².
Distance = speed × time. At 60 km/h for 3 hours the distance is 60 × 3 = 180 km. Keep the time in hours when the speed is in km/h.
Use matching units. For a small block, use grams and cm³ to get g/cm³. Do not mix grams with m³.
Speed is distance ÷ time. Density is mass ÷ volume. Pressure is force ÷ area.
Unit changes come before the rate, not after a wrong division. Forty centimetres is 0.4 metres, because 40 ÷ 100 = 0.4. Thirty centimetres is 0.3 metres. The area is 0.4 × 0.3 = 0.12 square metres. Dividing the force by 0.12 is then a pressure in N/m².
You can check the area in square centimetres and convert that. A square metre is 100 × 100 = 10000 square centimetres, so you divide the square-centimetre area by 10000. Squaring the length factor is essential. Using 100 once would convert a length, not an area.
Method: 1. Convert each length into the unit the answer needs. 2. Remember that area converts by the square of the length factor. 3. Convert time using 60, not using 10 or 100. 4. Only then divide or multiply to find the rate or the distance.
Speed, density and pressure all have the same shape: one quantity is another quantity divided by a third. Speed is distance over time, density is mass over volume and pressure is force over area. Each formula can be rearranged. For speed, distance is speed times time and time is distance over speed. The same pattern gives mass as density times volume and force as pressure times area.
A formula triangle helps if you draw it carefully, with the single quantity on top. The units are your second check. Speed in km/h is kilometres per hour, so the distance must be in kilometres and the time in hours. Density in g/cm^3 needs mass in grams and volume in cubic centimetres. Pressure in N/m^2 needs force in newtons and area in square metres.
Method: 1. Write the formula you need, rearranged if necessary. 2. Check that every number is in the unit the formula expects. 3. Substitute and calculate, keeping the full calculator display. 4. Write the answer with the correct compound unit.
Tip: If the answer unit has a slash, such as km/h or g/cm cubed, the top unit goes with the top quantity and the bottom unit goes with the bottom quantity.
Time in a speed question must be in hours if the speed is per hour. Convert minutes by dividing by 60. So 45 minutes is 0.75 hours and 1 hour 45 minutes is 1.75 hours, not 1.45. If the time is 2 hours 20 minutes, write it as 21/3 hours to avoid rounding errors, and let the calculator do the multiplying.
Average speed for a whole journey is the total distance divided by the total time. It is not the mean of the speeds. If a car travels 48 km at 24 km/h and then 48 km at 48 km/h, the times are 2 hours and 1 hour, so the average is 96/3 = 32 km/h, not 36. The slower stage takes longer, and so it has more effect on the average.
Method: 1. Convert every time to hours. 2. Find the time for each stage using time equals distance over speed. 3. Add the distances and add the times. 4. Divide total distance by total time.
To find the density of a mixture, find the total mass and the total volume. Do not average the two densities, because the amounts may not be equal. For 40 cm^3 of copper with density 8.96 g/cm^3 and 60 cm^3 of zinc with density 7.14 g/cm^3, the masses are 358.4 g and 428.4 g. The total is 786.8 g in 100 cm^3, so the density is 7.868 g/cm^3.
Metal densities are in g/cm^3 and building materials in kg/m^3. To change between them, remember 1 g/cm^3 = 1000 kg/m^3. Volumes of solids come from the usual formulas, such as length times width times height for a cuboid, or π r^2 h for a cylinder. Mass in the question may need converting to tonnes: 1 tonne is 1000 kg.
Method: 1. Find the volume of the solid using the correct formula. 2. Multiply volume by density to find mass, keeping units consistent. 3. For a mixture, add masses and add volumes before dividing. 4. Convert units at the end if the question asks for a different unit.
Pressure is force divided by area. If the force is in newtons and the area in square metres, the pressure is in N/m^2. Face areas are often given in cm^2, so convert by dividing by 10 000, since 1 m^2 = 10 000 cm^2. A block of fixed weight gives the greatest pressure on its smallest face and the least pressure on its largest face.
Conversion of a compound unit changes the top unit and the bottom unit separately. To change 12.5 m/s into km/h, multiply by 3600 to get metres per hour, then divide by 1000 to get kilometres per hour. This is the same as multiplying by 3.6. A common check is that 1 m/s is a little less than 4 km/h. Square units need squared conversion factors.
Method: 1. Convert area to square metres before calculating pressure in newtons per square metre. 2. Use the smallest face for the largest pressure and the largest face for the smallest pressure. 3. For speed in m/s to km/h, multiply by 3.6. 4. For area conversions, square the length conversion factor.
Tip: Multiply by 3.6 to go from m/s to km/h and divide by 3.6 to go back.
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