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M8.3MechanicsFoundation

Quantities and Units

Mechanics is built on SI units. Knowing the base quantities, their units, and the difference between scalars and vectors keeps your equations consistent and your answers correctly labelled.

20 min Modelling in Mechanics
Edexcel Mechanics Year 1 — full playlist (Zeeshan Zamurred)Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Know the SI base units used in mechanics
  • Distinguish scalar and vector quantities
  • Use consistent units in calculations
  • Recognise derived units like the newton
1

SI units

Mechanics uses SI units: length in metres (m), time in seconds (s), and mass in kilograms (kg). Quantities derived from these include velocity (m/s), acceleration (m/s²) and force in newtons (N).

m, s, kg  ⇒  m/s, m/s2, N=kg⋅m/s2\text{m, s, kg} \;\Rightarrow\; \text{m/s}, \ \text{m/s}^2, \ \text{N} = \text{kg·m/s}^2
Base units and key derived units.
2

Scalars and vectors

A scalar\textbf{scalar} has magnitude only (distance, speed, mass, time). A vector\textbf{vector} has magnitude and direction (displacement, velocity, acceleration, force). Pairing them up — distance/displacement, speed/velocity — is a common exam point.

Tip — Speed is a scalar; velocity is its vector partner. Same number, but velocity has direction.

3

Consistent units

Always convert to consistent SI units before calculating (e.g. km/h to m/s, grams to kg). Mixing units is one of the most common sources of wrong answers.

Example 1Convert 36 km/h to m/s.
1Divide by 3.6: 36÷3.636 \div 3.6.
Answer1010 m/s

Formula recap

length: m,  time: s,  mass: kg\text{length: m, \ time: s, \ mass: kg}
SI base units.
N=kg⋅m/s2\text{N} = \text{kg·m/s}^2
The newton (derived).
scalar: size; vector: size + direction\text{scalar: size; vector: size + direction}
The key distinction.

Common mistakes to avoid

Calculating with mixed units (e.g. km/h with metres).
Convert everything to consistent SI units first.
Calling velocity a scalar.
Velocity is a vector; speed is the scalar.

Key takeaways

  • SI base units: metres, seconds, kilograms.
  • Force is in newtons (N = kg·m/s²).
  • Scalars have size only; vectors also have direction.
  • Always use consistent units before calculating.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 4 lessons

Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.