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Quantities and S.I. units in mechanicsEdexcel A-Level Maths: Revision notes

Section 1

Fundamental quantities and units

Mechanics uses the S.I. system. The three fundamental (base) quantities and their units are:

  • length: metre (m)
  • time: second (s)
  • mass: kilogram (kg) Every other quantity in mechanics is derived from these. Always check that all values in a calculation are in S.I. units before substituting.
Key termsS.I.fundamental quantityderived quantity
Common mistake

Using kg and g, or km and m, in the same calculation without converting.

Section 2

Derived quantities and units

Common derived quantities:

  • velocity and speed: m s−1^{-1} (displacement or distance divided by time)
  • acceleration: m s−2^{-2} (change in velocity divided by time)
  • force: newton, N, where 11 N =1=1 kg m s−2^{-2}
  • weight: the force of gravity on a body, W=mgW=mg, measured in N
  • moment: force ×\times perpendicular distance, measured in N m, which is kg m2^2 s−2^{-2} Mass is measured in kg, but weight is a force measured in N. Take g=9.8g=9.8 m s−2^{-2} unless told otherwise.
Key termsvelocityaccelerationforceweightmomentnewton
Common mistake

Giving weight in kg. Weight is a force in N; kg is the unit of mass.

Section 3

Converting units

To convert km h−1\text{km h}^{-1} to m s−1\text{m s}^{-1}, multiply by 10003600=13.6\frac{1000}{3600}=\frac{1}{3.6}; to convert m s−1\text{m s}^{-1} to km h−1\text{km h}^{-1}, multiply by 3.63.6. Examples:

  • 7272 km h−1=72÷3.6=20^{-1}=72\div3.6=20 m s−1^{-1}
  • 2525 m s−1=25×3.6=90^{-1}=25\times3.6=90 km h−1^{-1}
  • 1515 minutes =900=900 s, so 5.45.4 km in 15 minutes is 5400900=6\frac{5400}{900}=6 m s−1^{-1} Convert each unit separately: km to m, h to s. Sense check: a speed in m s−1^{-1} is a smaller number than the same speed in km h−1^{-1}.
Key termsunit conversion
Exam tip

Multiplying by 3.6 makes a speed bigger (m s−1^{-1} to km h−1^{-1}); dividing makes it smaller.

Common mistake

Dividing by 60 once: an hour is 3600 seconds, not 60.

Section 4

Modelling assumptions

A model simplifies a real situation so that it can be analysed with mathematics. Learn the standard terms:

  • particle: the object has mass but negligible size, so rotation and dimensions are ignored
  • rod: a long object with negligible thickness; a lamina: a flat object with negligible thickness
  • smooth: no friction; rough: friction acts
  • light: no mass (e.g. a light string or pulley)
  • inextensible string: does not stretch; the tension is the same throughout a light string
  • air resistance negligible; uniform: mass evenly spread so weight acts at the centre
  • gravity constant: g=9.8g=9.8 m s−2^{-2} is the same at all heights reached Say what each assumption allows you to ignore, and be specific: 'the stone is a particle so its size does not matter'.
Key termsmodelparticlesmoothlightinextensibleuniformlamina
Exam tip

Quote the effect: 'air resistance is negligible, so the only force on the stone is its weight'.

Section 5

Worked example

A runner covers 400400 m in 5050 s at a constant speed. Find the speed in m s−1^{-1} and in km h−1^{-1}. Speed =40050=8=\frac{400}{50}=8 m s−1^{-1}. In km h−1^{-1}: 8×3.6=28.88\times3.6=28.8 km h−1^{-1}. Her mass is 60 kg: weight =60×9.8=588=60\times9.8=588 N. State the assumption that lets us treat her as a single point: she is modelled as a particle.

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Quantities and S.I. units in mechanics

  1. A car of mass 1200 kg travels along a straight horizontal road at a constant 7272 km h−1^{-1}.
    Find the weight of the car, taking g=9.8g=9.8 m s−2^{-2}, and state its unit.2 marks
  2. A cyclist of mass 70 kg travels a distance of 5.4 km in a time of 15 minutes along a straight track at a constant speed.
    Find the weight of the cyclist, taking g=9.8g=9.8 m s−2^{-2}, and express the unit of weight in terms of the S.I. base units kg, m and s.2 marks
  3. A stone of mass 0.4 kg is dropped from the top of a cliff and hits the sea at a speed of 29.729.7 m s−1^{-1}. The stone is modelled as a particle moving vertically under gravity only.
    State three modelling assumptions that are being made about the stone and its motion.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).