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 Video by Zeeshan Zamurred Modelling in Mechanics

Edexcel Mechanics Year 1 — full playlist (Zeeshan Zamurred)Watch the full walkthrough 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

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 \Rightarrow m/s, m/s^{2}, N = kg\cdotm/s^{2}

Base units and key derived units.

Scalars and vectors

A $scalar$ has magnitude only (distance, speed, mass, time). A $vector$ 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.

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.

1Divide by 3.6:

36 \div 3.6

Answer

10

m/s

Formula recap

length: m, time: s, mass: kg

SI base units.

N = kg\cdotm/s^{2}

The newton (derived).

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.

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