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M8.4MechanicsCore

Working with Vectors

Mechanics quantities like velocity and force are vectors, written in i–j form. Adding them, and finding magnitude and direction, are exactly the vector skills from Pure — now applied to motion and forces.

25 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

  • Write mechanics vectors in i–j form
  • Add and subtract vectors in components
  • Find the magnitude (e.g. speed) of a vector
  • Find the direction of a vector
1

i–j form in mechanics

Forces, velocities and displacements are written using (horizontal) and (vertical) unit vectors, e.g. a velocity m/s. Combine them by adding components, just as in Pure.

2

Magnitude

The of a vector is found with Pythagoras. For a velocity vector, the magnitude is the ; for a force, it is the size of the force.

Magnitude — e.g. speed from a velocity vector.
1.
Answer m/s
3

Direction

The direction is the angle the vector makes, found with of the components — typically measured from the positive direction. A sketch ensures you get the correct angle.

Direction of .

Tip — Magnitude of a velocity vector is the speed; the direction is the bearing/angle of travel.

Formula recap

Vector in i–j form.
Magnitude (e.g. speed).
Direction.

Common mistakes to avoid

Adding i and j components together.
Keep components separate: add i to i and j to j.
Confusing speed with velocity.
Speed is the magnitude of the velocity vector.

Key takeaways

  • Mechanics vectors are written in i–j form and added componentwise.
  • Magnitude = √(a² + b²); for velocity this is the speed.
  • Direction = tan⁻¹(b/a) — sketch to place the angle.

Test yourself

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