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8.1MechanicsStretch

Vectors in Kinematics

Motion in two dimensions is described with vectors. Position, velocity and acceleration become vector quantities, and the constant-acceleration (suvat) equations work in vector form.

24 min Further Kinematics
Edexcel A Level Maths: 8.1 Vectors in Kinematics (Part 1)Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Use position, velocity and acceleration vectors
  • Apply suvat in vector form
  • Find displacement and velocity at a time
  • Work with i, j components
1

Vector suvat

For constant acceleration, the suvat equations hold as vectors. For example v=u+at\mathbf{v} = \mathbf{u} + \mathbf{a}t and s=ut+12at2\mathbf{s} = \mathbf{u}t + \tfrac12\mathbf{a}t^2, each applied component by component.

v=u+at,s=ut+12at2\mathbf{v} = \mathbf{u} + \mathbf{a}t, \quad \mathbf{s} = \mathbf{u}t + \tfrac12\mathbf{a}t^2
suvat in vector form.
Example 1A particle has u=3i+j\mathbf{u} = 3\mathbf{i} + \mathbf{j} and a=i−2j\mathbf{a} = \mathbf{i} - 2\mathbf{j}. Find v\mathbf{v} at t=2t = 2.
1v=(3i+j)+2(i−2j)\mathbf{v} = (3\mathbf{i}+\mathbf{j}) + 2(\mathbf{i}-2\mathbf{j}).
2=5i−3j= 5\mathbf{i} - 3\mathbf{j}.
Answer
5i−3j5\mathbf{i} - 3\mathbf{j}

Tip — Apply each suvat equation separately to the i and j components.

Formula recap

v=u+at\mathbf{v} = \mathbf{u} + \mathbf{a}t
Velocity.
s=ut+12at2\mathbf{s} = \mathbf{u}t + \tfrac12\mathbf{a}t^2
Displacement.

Common mistakes to avoid

Adding the magnitudes of vectors directly.
Work component by component.
Forgetting suvat only applies for constant acceleration.
Use calculus methods when acceleration varies.

Key takeaways

  • Position, velocity, acceleration are vectors.
  • suvat holds in vector form for constant acceleration.
  • Work component by component (i and j).

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

  1. In vector kinematics, velocity is found from:

    • u+at\mathbf{u} + \mathbf{a}t
    • ut\mathbf{u}t
    • 12at2\tfrac12\mathbf{a}t^2
    • at2\mathbf{a}t^2
    Show answer and explanation

    Answer: u+at\mathbf{u} + \mathbf{a}t

    Vector suvat.

  2. suvat in vector form requires acceleration to be:

    • constant
    • zero
    • variable
    • large
    Show answer and explanation

    Answer: constant

    Otherwise use calculus.

  3. With u=3i+j\mathbf{u}=3\mathbf{i}+\mathbf{j}, a=i−2j\mathbf{a}=\mathbf{i}-2\mathbf{j}, v\mathbf{v} at t=2 is:

    • 5i−3j5\mathbf{i}-3\mathbf{j}
    • 5i+3j5\mathbf{i}+3\mathbf{j}
    • 4i−j4\mathbf{i}-\mathbf{j}
    • 3i+j3\mathbf{i}+\mathbf{j}
    Show answer and explanation

    Answer: 5i−3j5\mathbf{i}-3\mathbf{j}

    u + 2a.

  4. Vector equations are applied:

    • component by component
    • to magnitudes only
    • after adding lengths
    • randomly
    Show answer and explanation

    Answer: component by component

    i and j separately.

  5. Displacement under constant acceleration is:

    • ut+12at2\mathbf{u}t + \tfrac12\mathbf{a}t^2
    • u+at\mathbf{u} + \mathbf{a}t
    • at\mathbf{a}t
    • ut\mathbf{u}t
    Show answer and explanation

    Answer: ut+12at2\mathbf{u}t + \tfrac12\mathbf{a}t^2

    Vector suvat.

Next step

Check your understanding

Work through questions on Vectors in Kinematics. Use the feedback to decide what needs another look.

3 past-paper questions · 11 marks

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