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Kinematics: A Level Maths knowledge organiser

Everything to know about kinematics on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Displacement
Distance in a given direction from a starting point.
Velocity
Rate of change of displacement: speed with a direction.
Acceleration
Rate of change of velocity.
suvat
The five constant-acceleration equations linking s, u, v, a and t.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Constant accelerationIn the formula booklet: Edexcel, AQA, OCR\(v=u+at,\) \(s=ut+\tfrac12at^2,\) \(s=vt-\tfrac12at^2,\) \(s=\tfrac12(u+v)t,\) \(v^2=u^2+2as\)
… in vectorsIn the formula booklet: AQA, OCR\(\mathbf v=\mathbf u+\mathbf at,\) \(\mathbf r=\mathbf ut+\tfrac12\mathbf at^2\)
Variable acceleration\(v=\frac{dr}{dt},\) \(a=\frac{dv}{dt}=\frac{d^2r}{dt^2},\) \(r=\int v\,dt,\) \(v=\int a\,dt\)
Projectiles (speed \(U\), angle \(\alpha\))\(x=Ut\cos\alpha,\) \(y=Ut\sin\alpha-\tfrac12gt^2\)
Speed = \(|\mathbf v|\); velocity–time graph: gradient = acceleration, area = displacement

Worked example

A car starts from rest and accelerates at 2 m s⁻² for 5 s. Find its speed and the distance travelled.

  1. v = u + at = 0 + 2 × 5
  2. s = ut + ½at² = 0 + ½ × 2 × 25

Answer: v = 10 m s⁻¹ and s = 25 m

Common mistakes

  • Mechanics: too many significant figures after using g = 9.8
  • Area under a v–t graph read as acceleration
  • Distance vs displacement
  • Sign convention changed mid-question

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

  • Build simple mechanics models by stating assumptions such as treating an object as a particle, a string as light and inextensible and a surface as smooth.
  • Solve multi-stage constant acceleration problems, such as a car that accelerates then travels at constant speed, by linking the stages through shared quantities.
  • Differentiate displacement to find velocity and velocity to find acceleration when motion is given as a function of time, and interpret the results.
  • Model horizontal projection, such as a ball rolled off a table, treating the horizontal and vertical motion separately with constant velocity and constant acceleration.
  • Derive and use general formulae for projectile motion, such as the range and the equation of the trajectory, and use them to find launch angles.
  • Differentiate and integrate vectors with respect to time, such as finding velocity from r = 3t² i + (4t − t³) j, using initial conditions.

The printable sheet

Kinematics knowledge organiser for A Level Maths: one A4 page of key definitions, formulas, a worked example and common mistakes
Kinematics knowledge organiser (A Level Maths), A4. Download the PDF.

Revise it next

Other A Level Maths topics: Proof · Algebra and functions · Coordinate geometry · Sequences and series · Trigonometry · Exponentials and logarithms · Differentiation · Integration · Numerical methods · Vectors · Sampling and data · Probability · Binomial and normal distributions · Hypothesis testing · Forces and Newton's laws · Moments · All A Level Maths organisers