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LearnYMA01WME01 · Mechanics 1Mathematical models in mechanicsQuantities, units and evaluating models
Mathematical models in mechanics · Subtopic 2 of 2

Quantities, Units and Evaluating Models

Mechanics works in SI units: metres, kilograms, seconds and the newtons built from them. Convert before you calculate. Some quantities are scalars (size only) and some are vectors (size and direction). Once a model gives an answer, ask what it ignored and how that would change the result.

Edexcel YMA01 WME01Edexcel 9MA0 Paper 3AQA 7357 Paper 2≈ 25 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Use SI units and convert, e.g. km h⁻¹ to m s⁻¹.
  • Tell scalars from vectors.
  • Use W=mgW=mg with g=9.8g=9.8 m s⁻².
  • Explain how a model's assumptions affect its answer and suggest improvements.
Pause and think

A model says a dropped stone takes 2.02.0 s to fall. A real stone takes 2.12.1 s. Is the model wrong?

Section 2 of 14

Core idea

Start hereA spacecraft lost to units

In 1999 NASA's Mars Climate Orbiter was destroyed because one team worked in pound-force seconds and another in newton seconds. Units are not decoration: mixing them gives answers that are wrong by large factors.

The big idea

SI units: m, kg, s; newton 1 N=1 kg m s−21\text{ N}=1\text{ kg m s}^{-2}. Convert everything first. km h−1^{-1} ÷ 3.6 = m s−1^{-1}. Weight W=mgW=mg, g=9.8g=9.8 m s−2^{-2}.

1. Base and derived units

Converting km/h to m/s: divide by 3.6
2040608010012051015202530350speed (km/h)speed (m/s)m/s = km/h ÷ 3.636 km/h = 10 m/s72 km/h = 20 m/s
1 km/h is 1000 m in 3600 s, so multiply by 10003600=13.6\tfrac{1000}{3600}=\tfrac1{3.6}.
Why ÷ 3.6
  1. 1 km h−1=1000 m3600 s1\text{ km h}^{-1}=\frac{1000\text{ m}}{3600\text{ s}}
    1 km = 1000 m; 1 h = 3600 s.
  2. =13.6 m s−1=\frac1{3.6}\text{ m s}^{-1}
    Simplify the fraction.
Worked exampleConversions

Convert 72 km h−1^{-1}, 450 g (and find its weight), 2.5 minutes.

Goal
SI values.
Strategy
Standard factors.
  1. 72÷3.6=20 m s−172\div3.6=20\text{ m s}^{-1}
    Speed.
  2. 0.45 kg; W=0.45×9.8=4.41 N0.45\text{ kg};\ W=0.45\times9.8=4.41\text{ N}
    Mass in kg, then weight.
  3. 2.5×60=150 s2.5\times60=150\text{ s}
    Time.
Answer2020 m s−1^{-1}; 4.414.41 N; 150150 s.
✓ Check20×3.6=7220\times3.6=72 ✓.
Exam tipAccuracy With g=9.8g=9.8, give answers to 2 or 3 significant figures.
Common misconceptionMass vs weight Mass in kg; weight is a force in N.
Pause and think

Convert 15 m s−1^{-1} to km h−1^{-1}.

Summary

  • SI throughout.
  • ÷3.6; W=mgW=mg.
Key words
Newton
Force giving 1 kg an acceleration of 1 m s−2^{-2}.
HistoryThe metre from the Earth. In 1791 the French Academy of Sciences defined the metre as one ten-millionth of the distance from the North Pole to the equator through Paris. Today it is defined by the speed of light, but the size barely changed.
Fun factA 125125 million dollar unit slip. In 1999 NASA lost the Mars Climate Orbiter because one team's software used pound-force seconds while another expected newton-seconds. The spacecraft flew too close to Mars and was destroyed.
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