A Level Maths: Kinematics: Variable Acceleration 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.
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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:
- Kinematics — Constant Acceleration (SUVAT)}}: the simpler constant-acceleration case provides essential intuition
- Differentiation — needed to find velocity and acceleration from displacement
- Integration — needed to find displacement from velocity
A Level Maths kinematics with variable acceleration is the calculus side of mechanics. When acceleration is not constant — when it depends on time, for example — SUVAT no longer applies, and you use Differentiation and Integration to relate displacement, velocity, and acceleration. This is one of the cleanest applications of calculus in the course.
The fundamental relationships are: velocity is the time-derivative of displacement ($v = \frac{ds}{dt}$), and acceleration is the time-derivative of velocity ($a = \frac{dv}{dt}$). Equivalently, displacement is the time-integral of velocity ($s = \int v \, dt$) and velocity is the time-integral of acceleration ($v = \int a \, dt$). Given any one of the three (as a function of time), you can find the others by differentiating or integrating, applying initial conditions to fix any constants of integration. You handle problems involving objects starting from rest, returning to a starting position, momentarily stationary ($v = 0$), or reaching maximum velocity ($a = 0$).
Kinematics with variable acceleration 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: do not confuse 'momentarily at rest' ($v = 0$) with 'maximum velocity' ($a = 0$) — they correspond to different equations being zero; when integrating to find displacement, you ALWAYS need a constant of integration that must be determined from initial conditions; if a question asks for distance travelled (not displacement) and the object changes direction, you need to split the integral at the turning points; and the units of time in your function must match the units in the question (seconds vs minutes).