A-Level Maths: Mechanics
Mechanics is applied calculus and vectors under exam pressure: model the situation, resolve the forces, pick the right kinematic tool. This quiz spans the full mechanics strand of the prescribed content with fully specified numerical scenarios throughout.
The kinematics questions cover both regimes the specification demands. Constant acceleration runs through SUVAT: extracting a = 4 m/s² from v² = u² + 2as for a car accelerating over 100 m. Variable acceleration runs through calculus: integrating v = 3t² − 4t + 2 for displacement over three seconds, integrating a = 6t − 2 from rest for velocity, and differentiating the position t³ − 6t² + 9t to find the two instants where the particle is at rest — the factorised quadratic giving t = 1 and t = 3.
Projectiles appear twice: the ground-level launch at 20 m/s and 30°, testing the constant horizontal velocity, the 2.04 s flight time and the tempting-but-wrong maximum height, and the horizontal launch from a 49 m cliff, where the fall time √(2h/g) = √10 decouples from the horizontal range of 31.6 m.
The forces questions cover the specification's named systems: Newton's three laws matched to scenarios, the connected-particle pulley with masses 3 kg and 5 kg (acceleration 2.45 m/s² from the difference over the sum), the limiting friction condition P > μmg in both numeric and symbolic forms, and the angled-pull problem where the 10 N force's vertical component reduces the normal reaction to 14.6 N — the resolution step that separates mechanics marks from arithmetic.
Every numerical answer in the set was independently recomputed during verification, and two question stems were reworded for full self-containment. Explanations resolve forces and show the substitutions explicitly, in the diagram-free but complete style the written solutions demand.
- Apply SUVAT equations and calculus-based kinematics correctly by regime
- Analyse projectile motion by resolving into independent components
- Solve connected-particle pulley systems with Newton's second law
- Use the limiting friction condition F ≤ μR in numeric and symbolic forms
- Resolve angled forces to find normal reactions and net effects
Topic scope follows sections P–S (Quantities and units in mechanics; Kinematics; Forces and Newton's laws; Moments) of the DfE's prescribed AS and A level mathematics subject content — 100% common across all exam boards: SUVAT and calculus kinematics, projectiles, Newton's laws, connected particles, friction and moments.