A Level Maths: Vector Mechanics Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Variable Acceleration in Two Dimensions (OCR)
- Variable Acceleration in Two Dimensions (Edexcel)
- Constant Acceleration in Two Dimensions (OCR)
- Constant Acceleration in Two Dimensions (Edexcel)
- Forces and Motion in 3 Dimensions (OCR)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Vectors — 2D vectors are essential
- Kinematics — Constant Acceleration (SUVAT)}}: scalar kinematics provides the patterns
- Resolving Forces and Newton's Second Law (F = ma) — force analysis foundation
- Differentiation}} and {{Integration — needed for variable acceleration
A Level Maths vector mechanics combines Vectors with mechanics, using vectors to describe forces, velocities, and accelerations in two dimensions. Vectors give you a cleaner, more powerful framework for analysing motion and forces in 2D than scalar methods, and the techniques here are foundational for the more advanced mechanics work later.
You handle forces, velocities, and accelerations as 2D vectors using $\mathbf{i}, \mathbf{j}$ notation. Newton's second law in vector form, $\mathbf{F} = m\mathbf{a}$, applies in BOTH directions simultaneously, so you only ever need one equation. You handle problems with constant velocity (where the net force is zero and the velocity vector is fixed), constant acceleration (where SUVAT generalises to vector form), and collisions and meetings (where two objects are at the same position at the same time). You find position vectors as functions of time, $\mathbf{r}(t) = \mathbf{r}_0 + \mathbf{u}t + \tfrac{1}{2}\mathbf{a}t^2$, and use these to find the time and position of meeting. You also handle resultant forces, equilibrium in 2D, and problems involving wind, currents, and similar effects.
Vector mechanics is part of the Mechanics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: for two particles to meet, their POSITION vectors must be equal at the same time $t$, not just one component or the velocity; the magnitude of a vector is found using Pythagoras on the components — do not just add them; vector SUVAT applies when acceleration is CONSTANT — for variable acceleration use vector calculus; and when finding the time of closest approach, set the derivative of the squared distance to zero, NOT the distance itself.