CCEA GCSE Further Mathematics Unit 2 Mechanics: a complete overview of kinematics, forces, friction, momentum and projectiles

Unit 2 Mechanics is one of the three optional units in CCEA GCSE Further Mathematics (specification 2330); candidates take two of the three. It applies the Pure unit's algebra, trigonometry and calculus to motion and force. This guide maps the unit, from the suvat equations to projectile motion, and shows the methods CCEA repeats. It is the index to the Mechanics dot points, each with worked CCEA-style questions and cross-links.

Kinematics with constant acceleration

Motion in a straight line at constant acceleration is described by the four suvat equations linking displacement, initial and final velocity, acceleration and time. Velocity-time graphs give acceleration as the gradient and displacement as the area, and vertical motion under gravity is handled by taking $a = g$ with a consistent positive direction. Listing the known quantities first is the habit that earns marks.

Kinematics with variable acceleration

When acceleration depends on time the suvat equations no longer apply, so calculus takes over. Differentiating displacement gives velocity and differentiating again gives acceleration; integrating reverses the chain, with each integration's constant fixed by an initial condition. This is where the Pure unit's calculus does real physical work.

Vectors in mechanics

Displacement, velocity, acceleration and force are vectors, written in component ($\mathbf{i}$ and $\mathbf{j}$) form. You add and subtract them component by component, multiply by scalars, and find the magnitude by Pythagoras and the direction by trigonometry. Adding force vectors gives the resultant, and the magnitude of velocity is speed.

Newton's laws and forces

Newton's second law, $F = ma$, relates the resultant force to mass and acceleration and is the heart of dynamics. Weight is $mg$ downward, a surface provides a normal reaction, and a particle in equilibrium has zero resultant force. The method is always to draw a force diagram, choose a positive direction, find the resultant, and apply the law.

Friction

On rough surfaces, friction opposes motion up to a maximum of $\mu R$, the limiting friction, where $\mu$ is the coefficient of friction and $R$ the normal reaction. Comparing the applied force with the limiting friction decides whether an object moves; if it does, friction acts at $\mu R$ and Newton's second law gives the acceleration.

Connected particles

Two particles joined by a light inextensible string, often over a smooth pulley, share the same acceleration and one tension throughout. Writing an equation of motion for each particle and solving simultaneously, usually by adding to eliminate the tension, gives the common acceleration and the string tension.

Momentum and impulse

Momentum is mass times velocity and is directed; impulse is the change in momentum, equal to force times time. In a collision with no external horizontal force, total momentum is conserved, so the total before equals the total after. When objects coalesce, they move off with one common velocity.

Projectiles

A projectile moves freely under gravity, and its curved path is analysed by resolving the launch velocity into horizontal and vertical components. The horizontal motion is constant velocity; the vertical motion is constant acceleration under gravity. The two share only the time of flight, which links the maximum height, the time, and the range.

How CCEA examines Mechanics

Mechanics rewards clear modelling: a labelled force diagram, a stated positive direction, the right equation, and careful signs. Calculus, trigonometry and simultaneous equations from the Pure unit appear throughout, so secure those first. Use the dot points below for specification-level detail and worked CCEA-style questions, then test yourself with the Unit 2 quiz.

Syllabus, dot point by dot point

Browse the full set at /ccea-gcse/further-mathematics/syllabus.

• Kinematics with constant acceleration
• Kinematics with variable acceleration
• Vectors in mechanics
• Forces and Newton's laws
• Friction
• Connected particles
• Momentum and impulse
• Projectiles

For the official specification

CCEA publishes the full specification (2330), past papers and mark schemes at ccea.org.uk. Always revise from the current specification and CCEA's own past papers, because question style is board-specific.