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A LevelMaths: MechanicsCIERevision Notes1. Mechanics Toolkit1.1 Quantities, Units & Modelling1.1.3 Derived Units

Derived Units (CIE A Level Maths: Mechanics)

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Derived Units

What are derived units?

  • Derived units for quantities such as velocity, acceleration and force etc. are combinations of S.I. units
    • Speed or Velocity = distance ÷ time = m/s or m s-1 (Velocity is just speed with direction)
    • Acceleration = velocity ÷ time = ms-1 /s = m/s2 or m s-2
    • Weight or Force = mass x acceleration = kg m s-2 or N (N = Newtons)

1-1-3-diagram-1

Worked example

1.1.3_WE_Derived Units_1

a) Convert the following into S.I. units

i) 72 km h-2                    ii)   50 cm per minute                   iii)   14 g cm-3      

         1-1-3-worked-solution-a

b) A cyclist takes 15 minutes to travel 2.54 km. Calculate the average speed in m s-1?

1-1-3-worked-solution-b

Examiner Tip

  • Watch out for exam questions using non S.I. units such as feet and inches or miles per hour.
  • Make sure you are confident converting between these derived units,
  • Remember speed is velocity without direction and weight is a force measured in Newtons, not a mass measured in kg.
  • If you ever forget a formula, use the units it is measured in to figure it out,
  • e.g. m/s = metres ÷ seconds = distance ÷ time = velocity.

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    Previous:1.1.2 Fundamental UnitsNext:1.1.4 Types of Force
    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.