AQA A-Level Maths: Mechanics Revision Guide

Mechanics is one of the two applied strands in AQA A-Level Maths, assessed alongside Statistics in Paper 3. For many students, Mechanics is the more approachable of the two because the problems describe real-world situations -- objects moving, forces acting, things falling under gravity. You can often visualise what is happening, which makes the maths feel more concrete.

That does not mean it is easy. Mechanics questions demand precise mathematical technique combined with careful physical reasoning. You need to set up problems correctly before you can solve them, and a single sign error or missing force can unravel an otherwise strong answer. This guide covers the key topics, common pitfalls, and exam technique you need to perform well in Section B of Paper 3.

How Mechanics Is Assessed

Mechanics forms Section B of Paper 3 (Statistics and Mechanics). Paper 3 is 2 hours long and worth 100 marks, split roughly equally between Statistics in Section A and Mechanics in Section B. You should aim to spend about 55--60 minutes on each section, allowing a few minutes for checking.

The questions in Section B typically increase in difficulty. Early questions may involve straightforward SUVAT or force resolution, while later questions often combine multiple concepts -- for example, a connected particles problem on a rough inclined plane that requires resolving forces, applying Newton's second law, and using the friction model.

It is worth noting that the SUVAT equations are provided in the AQA formula booklet, so you do not need to memorise them. However, you do need to memorise F = ma, W = mg, the friction model F = muR, and the moment formula. See the formula booklet guide for the full breakdown.

Kinematics

Kinematics is the study of motion without considering the forces that cause it. You describe how objects move using displacement, velocity, and acceleration.

Scalar and Vector Quantities

Before diving into equations, be clear on the distinction between scalar and vector quantities. Speed is a scalar -- it has magnitude only. Velocity is a vector -- it has magnitude and direction. Likewise, distance is scalar and displacement is vector. This distinction matters because velocity and displacement can be negative, indicating motion or position in the opposite direction to your chosen positive direction.

The SUVAT Equations

For motion with constant acceleration, you use the SUVAT equations:

• v = u + at
• s = ut + 1/2 at^2
• s = vt - 1/2 at^2
• v^2 = u^2 + 2as
• s = 1/2 (u + v)t

These are given in the formula booklet, so focus on knowing when and how to use them rather than memorising them. Each equation links four of the five SUVAT variables (s, u, v, a, t). Identify which three values you know and which one you want to find, then choose the equation that contains exactly those four variables.

The critical condition is that SUVAT equations only apply when acceleration is constant. If a question describes an object whose acceleration changes over time, you cannot use SUVAT -- you must use calculus instead.

Variable Acceleration and Calculus

When acceleration varies, the relationships between displacement, velocity, and acceleration are expressed using calculus:

• Velocity is the rate of change of displacement: v = ds/dt.
• Acceleration is the rate of change of velocity: a = dv/dt = d^2s/dt^2.
• Displacement is the integral of velocity: s = integral of v dt.
• Velocity is the integral of acceleration: v = integral of a dt.

When you integrate, remember to include a constant of integration and use initial conditions or boundary conditions to find its value.

Displacement-Time and Velocity-Time Graphs

You should be confident reading and interpreting these graphs:

• On a displacement-time graph, the gradient at any point gives the velocity. A straight line means constant velocity; a curve means the velocity is changing.
• On a velocity-time graph, the gradient gives the acceleration and the area under the graph gives the displacement. A straight line means constant acceleration (SUVAT applies); a curve means variable acceleration.

Forces and Newton's Laws

Newton's Three Laws

Newton's first law states that an object remains at rest or moves with constant velocity unless acted on by a resultant force. Newton's second law states that the resultant force on an object is equal to its mass times its acceleration: F = ma. Newton's third law states that for every action there is an equal and opposite reaction -- the forces act on different objects.

In exam questions, Newton's second law is by far the most frequently used. Almost every Mechanics question that involves finding an acceleration or a force will require you to apply F = ma in some form.

Common Forces

You need to recognise and correctly label the forces that act on objects:

• Weight (W = mg, acting vertically downwards). Use g = 9.8 m/s^2 unless the question states otherwise.
• Normal reaction (R, perpendicular to the surface of contact). The normal reaction is not always equal to the weight -- on an inclined plane, for instance, R = mg cos(theta).
• Tension (T, in a string or rope, pulling the object towards the string).
• Friction (F, opposing the direction of motion or the tendency to move, acting along the surface).
• Driving force and resistance (in problems involving vehicles).

Resolving Forces

When forces act at angles, you resolve them into perpendicular components -- usually horizontal and vertical, or parallel and perpendicular to an inclined plane. For a force of magnitude P acting at angle theta to the horizontal:

• Horizontal component: P cos(theta).
• Vertical component: P sin(theta).

On an inclined plane at angle theta to the horizontal, resolve parallel and perpendicular to the slope. The component of weight parallel to the slope (acting down the slope) is mg sin(theta), and the component perpendicular to the slope is mg cos(theta).

Equilibrium

An object is in equilibrium when the resultant force acting on it is zero. This means the object is either at rest or moving with constant velocity. To solve equilibrium problems, resolve forces in two perpendicular directions and set the sum of forces in each direction equal to zero.

Connected Particles

These problems involve two or more objects linked by a string, often passing over a pulley. The key principles are:

• If the string is light (massless) and inextensible, the tension is the same throughout the string and both objects have the same magnitude of acceleration.
• Apply F = ma to each object separately, using a consistent sign convention.
• Solve the resulting simultaneous equations.

Common setups include two particles connected by a string over a smooth pulley (Atwood's machine), a particle on a table connected to a hanging particle, and two objects connected by a tow bar.

Modelling Assumptions

Every mechanics problem involves simplifying assumptions. You need to understand what each one means:

• Particle: The object has mass but no size. Air resistance and rotation are ignored.
• Smooth: There is no friction.
• Rough: Friction acts. You will need the friction model.
• Light: The object has no mass (used for strings, rods, and pulleys).
• Inextensible: The string does not stretch, so connected objects have the same speed and acceleration.
• Rigid: The object does not bend or deform.

Examiners often ask you to comment on the validity of a modelling assumption. For example, "State one limitation of the model" or "Explain how the answer would change if the surface were rough." Be specific in your response -- do not just say "the model is not realistic." Explain what the assumption ignores and how it affects the result.

Friction

The friction model states that the frictional force F satisfies F <= muR, where mu is the coefficient of friction and R is the normal reaction force. When the object is on the point of moving or is already moving, friction takes its maximum value: F = muR.

For an object at rest, friction can take any value from zero up to muR, adjusting itself to maintain equilibrium. Only when the applied force exceeds the maximum possible friction does the object start to move.

On a rough inclined plane, you will often need to combine the friction model with force resolution. A typical problem might ask you to find the coefficient of friction given that an object is on the point of sliding, or to find the acceleration of an object sliding down a rough slope.

Always check whether the question says the surface is smooth or rough. If it says rough, friction must be included. If it says smooth, friction is zero. This is one of the most common sources of lost marks -- students either include friction when the surface is smooth or forget it when the surface is rough.

Moments

A moment measures the turning effect of a force about a point. The moment of a force about a point is the magnitude of the force multiplied by the perpendicular distance from the point to the line of action of the force:

Moment = F x d

where d is the perpendicular distance.

The Principle of Moments

For an object in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point. You can take moments about any point, but choosing your pivot wisely -- typically at the point where an unknown force acts -- eliminates that force from the equation and simplifies your working.

Uniform and Non-Uniform Rods

For a uniform rod, the weight acts at the midpoint. For a non-uniform rod, the weight acts at the centre of mass, which may not be the midpoint. The position of the centre of mass is usually given in the question or must be found.

Tilting Problems

Tilting occurs when one of the support reactions becomes zero. If a beam rests on two supports and you add a load that causes it to tilt about one support, the reaction at the other support drops to zero. Set the reaction at the lifting support to zero and take moments about the tilting support to solve the problem.

Projectiles

Projectile motion combines horizontal and vertical motion. The key principle is that horizontal and vertical components are independent of each other:

• Horizontally, there is no acceleration (ignoring air resistance), so the horizontal velocity remains constant.
• Vertically, the only force is gravity, so the acceleration is g = 9.8 m/s^2 downwards.

For a projectile launched with speed u at angle theta to the horizontal:

• Horizontal component of velocity: u cos(theta), constant throughout the motion.
• Vertical component of velocity: u sin(theta) initially, then changes due to gravity.

Apply the SUVAT equations separately to each direction. Use horizontal motion to find horizontal distances and times, and vertical motion to find heights and vertical velocities.

Common quantities to find:

• Time of flight: Set vertical displacement to zero (for a projectile returning to its launch height) and solve for t.
• Maximum height: Set vertical velocity to zero and solve for s.
• Range: Use the time of flight to calculate horizontal distance.

Be careful with signs. If you take upwards as positive, then a = -9.8 m/s^2 for the vertical component. Stick to your chosen convention throughout the problem.

Common Mistakes

These are the errors that cost students marks most frequently in Mechanics:

• Not drawing a force diagram. Even when the question does not ask for one, drawing a clear force diagram helps you identify all the forces and their directions. Without it, you are far more likely to miss a force or resolve incorrectly.
• Wrong sign convention. Choose a positive direction at the start and apply it consistently. If upwards is positive, acceleration due to gravity is -9.8, not +9.8.
• Forgetting to resolve on inclined planes. The component of weight down the slope is mg sin(theta), not mg. The normal reaction is mg cos(theta), not mg.
• Using SUVAT when acceleration is not constant. If the question gives acceleration as a function of time, you must use calculus.
• Using g = 10 instead of g = 9.8. Unless the question explicitly says "take g = 10", use g = 9.8 m/s^2.
• Confusing speed and velocity. Speed is always positive. Velocity can be negative. If a question asks for speed, give the magnitude of the velocity.
• Ignoring friction on rough surfaces. If the surface is described as rough, the friction force must appear in your force diagram and your F = ma equation.
• Assuming the normal reaction equals the weight. This is only true on a horizontal surface with no other vertical forces. On a slope or when other forces have a vertical component, you must calculate R separately.

Exam Technique for Mechanics

Strong exam technique can be the difference between a good mark and an excellent one. Here is how to approach Mechanics questions effectively.

Always draw a force diagram. This is the single most important habit. Mark all forces with their correct directions and label them clearly. Include the weight (always vertically downwards), the normal reaction (perpendicular to the surface), tension (along the string), and friction (opposing motion, along the surface).

Choose a positive direction and state it. Write it down at the start of your solution. For inclined plane problems, it is usually most convenient to take the direction of motion (or the direction up the slope) as positive.

Apply F = ma systematically. Resolve forces in your chosen direction, write down the resultant force, set it equal to ma, and solve. Show each step clearly. The examiner needs to see your method, not just your answer.

State modelling assumptions when relevant. If a question asks you to set up a model, mention the assumptions you are making (e.g., "modelling the car as a particle" or "assuming the string is light and inextensible").

Use exact values where appropriate. If the question gives values in surd form or involves exact trigonometric ratios, keep your answer exact. Only round at the end if the question asks for a specific number of significant figures or decimal places.

Check your answer makes physical sense. If you calculate a negative acceleration for an object that should be speeding up, or a coefficient of friction greater than 1 (unusual but not impossible), pause and check your working.

If a question says "take g = 9.8", use that value throughout. Do not switch to 9.81 or 10 partway through.

Prepare with LearningBro

LearningBro's A-Level Maths Mechanics course covers every topic in this guide with structured lessons and practice questions that mirror the style and difficulty of AQA Paper 3. Each lesson builds on the previous one, taking you from basic kinematics through to multi-step problems involving connected particles on rough inclined planes.

If you want to strengthen your problem-solving skills across all three papers, the A-Level Maths problem-solving course focuses on the techniques that help you tackle unfamiliar questions under exam conditions. And for targeted AQA preparation, the AQA exam preparation course combines timed practice with detailed mark scheme analysis so you know exactly what examiners are looking for.

For a complete breakdown of which formulas you need to memorise and which are provided in the exam, see the formula booklet guide.

Good luck with your revision. You have got this.