National 5MathsSQAApplications of MathematicsRevision NotesMeasurement SkillsUnits & QuantitiesSpeed, Time & Distance

Speed, Time & Distance (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Dan Finlay

Written by: Dan Finlay

Reviewed by: Roger B

Updated on

Speed, time & distance

How do I calculate speed?

  • Speed is a compound measure of how fast an object is moving

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

  • The formula is Speed equals Distance divided by Time

  • You can rewrite the speed as a conversion factor

    • Consider 10 metres per second

      • Rewrite as 1 second = 10 metres

Examiner Tips and Tricks

Make sure the units for distance and time are consistent with the units for speed. For example, if you want the speed in metres per second, then make sure the distance is in metres and the time is in seconds.

Worked Example

A runner completes a 10 km race in 45 minutes.

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

Answer:

Convert the units for the distance and time to match the units required for the speed

  • Multiply the distance by 1000 to convert km to metres

10 cross times 1000 equals 10 comma 000 space straight m

  • Multiply the time by 60 to convert from minutes to seconds

45 cross times 60 equals 2700 space seconds

Use Speed equals Distance divided by Time

table row cell Speed space end cell equals cell 10 comma 000 divided by 2700 end cell row blank equals cell 3.703703... space straight m divided by straight s end cell end table

Round to 3 significant figures

3.70 m/s

How do I calculate time using the speed?

  • Divide the distance by the speed

    • Time equals Distance divided by Speed

How do I calculate distance using the speed?

  • Multiply the time by the speed

    • Distance equals Time cross times Speed

Examiner Tips and Tricks

Using conversion factors means that you don't have to remember these formulas.

Worked Example

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.
Give your answer in seconds and round your answer to two decimal places.

Answer:

Rewrite as a conversion factor

1 second = 8.85 m

Divide the distance by the conversion factor to find the time

100 divided by 8.85 equals 11.299...

Round to 2 decimal places

11.30 s

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    Author
    Reviewer
    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Subject 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.

    Roger B

    Reviewer: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.