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11.6PureStretch

Modelling with Vectors

Vectors model anything with size and direction — velocity, displacement, force. This lesson applies the vector toolkit to real situations, where speed is a magnitude and direction is often a bearing.

25 min Video by Zeeshan Zamurred Vectors
Edexcel AS Level Maths: 11.6 Modelling with Vectors (Application)Watch the full walkthrough before the notes below.
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What you'll be able to do

  • Model displacement and velocity as vectors
  • Find speed as the magnitude of velocity
  • Use vectors with bearings
  • Find resultant displacement and position over time
1

Velocity and speed

Velocity is a vector (it has direction); is its magnitude (just a number). So a velocity of m/s corresponds to a speed of m/s.

Speed is the magnitude of the velocity vector.
1.
Answer m/s
2

Position over time

If an object starts at position and moves with constant velocity , its position after time is found by adding lots of the velocity.

Start position plus (time × velocity).
1.
Answer
3

Vectors and bearings

In navigation problems the direction is usually east and north. Convert a bearing into a direction angle, sketch it, and use components to find resultant displacements.

Tip — Sketch east as i and north as j, then break each leg of the journey into components before adding.

Formula recap

Speed = magnitude of velocity.
Position under constant velocity.
Usual navigation convention.

Common mistakes to avoid

Calling velocity and speed the same thing.
Velocity is a vector; speed is its magnitude (a scalar).
Adding time to the position instead of (time × velocity).
Position = r₀ + t·v — multiply the velocity by time first.

Key takeaways

  • Velocity is a vector; speed = |velocity|.
  • Position after time t: r = r₀ + t·v.
  • For bearings, take i = east, j = north and work in components.

Test yourself

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