Speed (Cambridge (CIE) IGCSE International Maths: Extended): Revision Note

• Look out for a mixture of units

  • Time can be given as minutes but common phrases like 'half an hour' (30 minutes) could also be used in the same question

  • Any mixed units should be those in common use and easy to convert, e.g. m to km etc

(a) A runner completes a 10 km race in three quarters of an hour.

Find the average speed of the runner in metres per second.
Round your answer to 3 significant figures.

As the answer must be in metres per second, convert the distance to metres, and the time to seconds

Multiply by 1000 to convert km to metres

10 km = 10 000 m

Write the time in minutes, you could calculate this as $\frac{3}{4}\times 60\mathrm{mins}$

Three quarters of an hour = 0.75 hrs = 45 mins

Multiply by 60 to convert minutes to seconds

45 × 60 = 2 700 seconds

Use the formula $\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

$\mathrm{Speed}=\frac{10000\mathrm{m}}{2700\mathrm{s}}=3.703703...\mathrm{m}/\mathrm{s}$

Round to 3 significant figures

3.70 m/s

(b) A sprinter's average speed when running 100 m is 8.85 m/s.

Calculate the total time taken in seconds for the sprinter to run 100 m.
Round your answer to the nearest hundredth of a second.

The units are already in metres, and metres per second, so do not need converting to reach an answer in seconds

Use the formula $\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

$8.85\mathrm{m}/\mathrm{s}=\frac{100\mathrm{m}}{\mathrm{Time}}$

Rearrange to make the time the subject
Multiply both sides by time, and then divide both sides by the speed

$\begin{array}{rcl}8.85\times \mathrm{Time}& =& 100\\ \mathrm{Time}& =& \frac{100}{8.85}\\ \mathrm{Time}& =& 11.29943503...\end{array}$

Round to the nearest hundredth of a second (2 decimal places)

11.30 s