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Derived Units (CIE A Level Maths: Mechanics)
Revision Note
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)
Worked example
a) Convert the following into S.I. units
i) 72 km h-2 ii) 50 cm per minute iii) 14 g cm-3
b) A cyclist takes 15 minutes to travel 2.54 km. Calculate the average speed in m s-1?
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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