MathsGradeUp logoMathsGradeUp
PhysicsGCSE, IGCSE & A Level

What is newton's second law?

Newton's second law states that the resultant force on an object equals its mass multiplied by its acceleration.

Newton's second law explained

The law only works with the resultant — the vector sum of every force acting. Draw a free-body diagram and resolve into perpendicular directions before substituting anything.
At A Level the law is written in terms of momentum: force equals rate of change of momentum, which handles varying-mass problems such as rockets.

Key formula

F=maF = ma

Worked example

A 1200 kg1200\,\text{kg} car accelerating at 2 m s−22\,\text{m s}^{-2} needs a resultant force of 2400 N2400\,\text{N}.

Examiner tip

Define a positive direction on your diagram and keep every substitution consistent with it; sign errors cost more marks here than arithmetic.

Newton's second law: common questions

Does F = ma apply when mass changes?
Not directly. Use force equals rate of change of momentum, which reduces to F = ma only for constant mass.
What happens when the resultant force is zero?
The object stays at rest or continues at constant velocity — that is Newton's first law, the special case of the second.

Related terms

Resultant force

The resultant force is the single force that has the same effect as all the forces acting on an object combined.

Momentum

Momentum is the product of an object's mass and velocity, and it is conserved in any collision or explosion with no external force.

Acceleration

Acceleration is the rate of change of velocity with time, measured in metres per second squared.

Practise physics on MathsGradeUp

Take newton's second law from a definition to full marks with exam-board question banks, revision notes and instant step-by-step feedback from Study Coach.

Physics revision notesPractice questionsCreate a free account

Related on MathsGradeUp

Keep studying

Practise it