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Speed (Cambridge (CIE) IGCSE International Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: CoreCambridge (CIE) International Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 1Edexcel Maths A: HigherCambridge (CIE) Maths: ExtendedCambridge (CIE) Maths: Core

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Speed

What is speed?

  • Speed is equal to distance divided by time

  • Speed is commonly measured in metres per second (m/s) or kilometres per hour (km/h)

    • The units indicate speed is distance per time
      Speed equals Distance over Time

  • 'Speed' (in this formula) means 'average speed'

  • The formula can be rearranged to

    • Time space equals fraction numerator space Distance over denominator Speed end fraction

    • Distance equals Speed cross times Time

  • In harder problems there are often two journeys or two parts to one longer journey

What is a formula triangle?

  • A formula triangle shows the relationship between the different measures in a compound formula 

  • They can be useful if you are less confident with rearranging formulas

  • For Speed, Distance and Time:

Formula triangle: Speed, Distance, Time

  • If you are calculating a variable on the top of the triangle, multiply the two variables on the bottom

    • For example,  Distance space equals space Speed space cross times space Time 

  • If you are calculating a variable on the bottom of the triangle, divide the top by the other variable on the bottom

    • For example,  Speed space equals space Distance space divided by space Time  and  Time space equals space Distance space divided by space Speed

Examiner Tips and Tricks

  • 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

Worked Example

(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 3 over 4 cross times 60 space 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 Speed equals Distance over Time

Speed space equals fraction numerator 10000 space straight m space over denominator 2700 space straight s end fraction equals 3.703703... space straight m divided by straight 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 Speed equals Distance over Time

8.85 space straight m divided by straight s equals fraction numerator 100 space straight m over denominator Time end fraction

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

table row cell 8.85 cross times Time space end cell equals cell space 100 end cell row Time equals cell fraction numerator 100 over denominator 8.85 end fraction end cell row cell Time space end cell equals cell space 11.29943503... end cell end table

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

11.30 s

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.