A-Level Physics: Mechanics Revision Guide with Worked Examples

A common September pattern: new Year 12s walk into physics thinking mechanics is just “harder GCSE.” It isn’t. Get forces, motion, energy, and momentum sorted properly now — not vaguely understood, actually sorted — and you’ll find the rest of the course clicks into place. Bodge it, and you’ll be fighting the same gaps in Year 13. So let’s get it right.

Motion and Kinematics

A frequent failure mode at A-Level: a student can recite all four SUVAT equations perfectly but can’t solve a basic projectile problem. The reason is almost always the same — they never really understood what the equations describe. So before we touch the maths, let’s nail the concepts.

Kinematics describes how objects move without worrying about what causes the motion. Three quantities matter here:

Displacement (s) is distance in a particular direction — a vector, measured in metres. Velocity (v) is how fast displacement changes (m/s). Acceleration (a) is how fast velocity changes (m/s²). Simple enough. But here’s where students slip up: velocity and speed aren’t the same thing. Velocity has direction. That matters.

The SUVAT equations govern motion with constant acceleration:

• v = u + at
• s = ut + ½at²
• v² = u² + 2as
• s = ½(u + v)t

Where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.

So how do you pick the right equation? Look at what’s missing. No time in the question? Use v² = u² + 2as. No final velocity? Use s = ut + ½at². The single best habit: write out what you know before touching any formula. Sounds obvious, but it stops so many errors. Most students don’t bother. They pay for it.

Displacement-time graphs: the gradient gives velocity, curved lines mean acceleration, horizontal lines mean stationary. Velocity-time graphs: the gradient gives acceleration, and the area under the curve gives displacement. Velocity-time graphs are arguably the more useful of the two — they pack in more information — but you need to be comfortable reading both.

Worked Example: Free Fall

A ball is dropped from rest from a height of 45m. Calculate: (a) the time taken to hit the ground, (b) the final velocity.

Given: u = 0 m/s (dropped from rest), s = 45m, a = 9.81 m/s² (gravity)

(a) Using s = ut + ½at²: 45 = 0 + ½(9.81)t² 45 = 4.905t² t² = 9.17 t = 3.03s

(b) Using v = u + at: v = 0 + 9.81 × 3.03 v = 29.7 m/s

Forces and Newton’s Laws

Newton’s Three Laws show up everywhere in A-Level Physics. Everywhere. You need these cold.

Newton’s First Law: An object stays at rest or moves with constant velocity unless a resultant force acts on it. This is inertia — objects resist changes in motion. No resultant force means no acceleration. That’s it.

Newton’s Second Law: F = ma. The resultant force equals mass times acceleration. Force is measured in Newtons (N). This one equation underpins about a third of mechanics questions, so if you’re shaky on rearranging it, fix that now.

Newton’s Third Law: When object A pushes on object B, object B pushes back on A with equal force in the opposite direction. Crucially, these paired forces act on different objects. Always. This is arguably the most misunderstood of the three laws — candidates routinely draw both forces acting on the same object, which makes equilibrium problems nonsense.

Resolving Forces

When multiple forces act on an object, you’ve got to resolve them into components. This is non-negotiable.

For a force F at angle θ to the horizontal: the horizontal component is Fcosθ, the vertical component is Fsinθ. If the resultant force is zero, the object’s in equilibrium — either stationary or moving at constant velocity.

Worked Example: Forces on a Slope

A 5kg block sits on a 30° slope. Calculate the component of weight acting down the slope and the normal reaction force. (g = 9.81 m/s²)

Weight W = mg = 5 × 9.81 = 49.05N (acting vertically downwards)

Component down slope = Wsin30° = 49.05 × 0.5 = 24.5N

Normal reaction N = Wcos30° = 49.05 × 0.866 = 42.5N

The normal reaction acts perpendicular to the slope, balancing the perpendicular component of weight.

A persistent mistake on inclined-plane questions: students mix up sine and cosine on slopes. The pattern: the component down the slope uses sin (that’s the angle at the bottom of your triangle), the component into the slope uses cos. Draw the triangle every single time. Candidates who sketch the geometry tend to get it right; those who guess which trig function to use get it wrong about half the time. Don’t guess.

Energy and Work

Work done (W) is energy transferred when a force moves an object: W = Fs cosθ, where F is force, s is displacement, and θ is the angle between them. When force and displacement are parallel, it simplifies to W = Fs. Measured in Joules.

Kinetic energy is energy from motion: KE = ½mv². Gravitational potential energy depends on position: GPE = mgh, where h is height above your chosen reference point.

Conservation of energy: energy can’t be created or destroyed, only transferred. In mechanics, this means total energy — KE plus PE plus any heat or sound — stays constant. Why does this matter? Because it gives you an alternative route into problems that’d be messy with forces alone.

Worked Example: Energy Conservation

A 2kg ball is thrown upwards with initial velocity 15 m/s. Calculate the maximum height reached.

Initial KE = ½mv² = ½ × 2 × 15² = 225J

At maximum height, all KE converts to GPE (velocity = 0).

GPE = mgh 225 = 2 × 9.81 × h h = 225/(2 × 9.81) = 11.5m

Momentum

Momentum (p) is mass × velocity: p = mv. It’s a vector — direction matters — measured in kg m/s.

Conservation of momentum: in a closed system with no external forces, total momentum before equals total momentum after. This works for collisions and explosions. For two objects:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where u is initial velocity, v is final velocity.

Impulse is change in momentum: Impulse = Δp = FΔt. A force applied over time changes an object’s momentum. The November 2023 AQA paper had a lovely question linking impulse to car safety features — crumple zones extend the collision time, reducing the force on passengers. Classic application.

Elastic vs Inelastic Collisions

Elastic collisions conserve both momentum and kinetic energy. Objects bounce apart. Inelastic collisions conserve momentum but not kinetic energy — some KE converts to heat, sound, deformation. If objects stick together, that’s perfectly inelastic.

A common student question: “How do I know which type it is?” Fair question. If the problem doesn’t tell you, assume inelastic unless objects are described as bouncing apart with no energy loss. Real collisions are almost always inelastic — billiard balls come close to elastic, but even they aren’t perfect.

Worked Example: Collision

A 1000kg car travelling at 20 m/s collides with a stationary 1500kg car. They stick together. Calculate their combined velocity after collision.

Before: p = m₁u₁ + m₂u₂ = (1000 × 20) + (1500 × 0) = 20000 kg m/s

After: p = (m₁ + m₂)v = 2500v

By conservation of momentum: 20000 = 2500v v = 8 m/s

Moments and Equilibrium

A moment is the turning effect of a force: Moment = Force × perpendicular distance from pivot. Get that word perpendicular stuck in your head.

Principle of moments: for an object in equilibrium, clockwise moments equal anticlockwise moments about any point. Any point — that’s useful, because sometimes choosing a clever pivot eliminates an unknown force from your equation entirely.

A couple is a pair of equal, opposite, parallel forces that produce rotation without translation. Torque = Force × perpendicular distance between the forces.

Worked Example: Balanced Beam

A 3m uniform beam of weight 100N is supported at its centre. A 40N weight hangs 1m from the left end. Where must a 60N weight hang to balance the beam?

Taking moments about the centre:

Clockwise moments = 40 × 1 = 40 Nm

Anticlockwise moments = 60 × d (where d is distance from centre)

For equilibrium: 40 = 60d d = 0.67m from centre (to the right)

Density and Pressure

Quick definitions here. Density: ρ = mass/volume (kg/m³). Pressure: P = Force/Area (Pascals, or N/m²). Pressure in fluids increases with depth: P = ρgh.

That last formula — P = ρgh — links nicely to the work you’ll do on gases and fluids later. Don’t skip it.

Common Mistakes in Mechanics

Examiner reports flag the same mechanics errors year after year. Avoid these and you’ll already be ahead of most candidates:

First, confusing mass and weight. Mass (kg) is quantity of matter. Weight (N) is gravitational force: W = mg. They’re not interchangeable. Then there’s sign errors with vectors — define a positive direction at the start and stick to it, or your momentum calculations will fall apart. Sound obvious? A large fraction of candidates still gets this wrong.

Using the wrong SUVAT equation happens when students don’t list their knowns first. Forgetting to resolve forces on slopes or at angles is epidemic. Mixing up elastic and inelastic — remember, momentum always conserves; KE only conserves in elastic collisions. And finally, unit inconsistencies: always work in SI units. Convert before you calculate, not after.

The single biggest predictor of success in mechanics questions is whether the student draws a diagram. Ignore anyone who tells you diagrams are optional. They aren’t. Every forces question, every collision, every slope — sketch it out. Two minutes of drawing saves ten minutes of confusion.

How to Use This Guide

The honest advice — and it might not be what you expect: don’t just read this. Reading physics notes five times won’t help you if you never actually work through problems yourself; that’s a well-documented failure pattern that leaves candidates bombing straightforward questions in the exam. Grab pen and paper, cover the solutions above, and attempt the worked examples properly before checking.

Then hit past papers. Mark schemes arguably teach you more than the questions do — they show you exactly how examiners allocate marks, step by step. When SUVAT clicks but momentum keeps tripping you up, focus your time on momentum. Be strategic.

If you’ve got gaps, come back to specific sections. And if something still isn’t landing after three or four attempts, that’s when you ask for help — not before you’ve properly wrestled with it yourself. That struggle is where the learning actually happens.

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