Apply Newton's laws of motion: use F equals ma to relate resultant force, mass and acceleration, work with weight, and analyse particles in equilibrium.

What this dot point is asking

Dynamics explains why objects accelerate, and CCEA GCSE Further Mathematics builds it on Newton's laws of motion. You must find the resultant force on a particle, apply $F = ma$ to relate that resultant to mass and acceleration, use weight as $mg$, work with the normal reaction from a surface, and analyse particles in equilibrium where the forces balance. Drawing a clear force diagram is the first and most important step.

Newton's laws

The three laws describe how forces affect motion. The first defines what happens with no resultant force, the second quantifies the effect of a resultant force, and the third pairs forces between bodies.

Applying F equals ma

The working method is always the same: draw a force diagram, choose a positive direction (usually the direction of acceleration), add up the forces in that direction to get the resultant, then set the resultant equal to $ma$.

For example, a $2$ kg particle pulled by $10$ N forward against a $4$ N resistance has resultant $10 - 4 = 6$ N, so $6 = 2a$ and $a = 3$ m/s$^2$.

Weight and normal reaction

Weight is the force of gravity on a mass, acting vertically downward, and is distinct from mass: mass is measured in kilograms, weight in newtons. A surface pushes back on an object resting on it with a normal reaction, perpendicular to the surface. On a horizontal surface with no vertical acceleration, the normal reaction balances the weight, so $R = mg$.

Equilibrium of a particle

A particle is in equilibrium when the resultant force is zero, so it stays at rest or moves at constant velocity. This means the forces balance in every direction, which gives equations you can solve for unknown forces.

Why this matters

Newton's laws are the heart of the Mechanics unit and the bridge between forces and kinematics: the second law supplies the acceleration that then feeds the suvat equations or the calculus methods. Equilibrium and the normal reaction set up the friction topic, and the third law underpins connected-particle problems with strings and pulleys. A disciplined force diagram and a clear choice of positive direction make every dynamics question tractable.