Newton's Laws of Motion

Newton’s three laws describe how forces affect the motion of objects.

Newton’s first law

An object remains at rest or continues to move at constant velocity unless acted on by a resultant force.

This means: no resultant force = no change in velocity. A moving object does not need a force to keep moving; it needs a force only to change speed or direction.

Newton’s second law

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.

$F = ma$

Symbol	Quantity	Unit
$F$	Resultant force	N
$m$	Mass	kg
$a$	Acceleration	m/s$^2$

Newton’s third law

When object A exerts a force on object B, object B exerts an equal and opposite force on object A. The two forces act on different objects, are the same type, and are equal in size but opposite in direction.

Worked example

A 1200 kg car has a resultant forward force of 3600 N. Calculate the acceleration.

$a = \frac{F}{m} = \frac{3600}{1200} = 3.0\text{ m/s}^2$

Worked example: third law

A swimmer pushes the pool wall backward with a force of 80 N. By Newton’s third law, the wall pushes the swimmer forward with a force of 80 N. The forces are equal in size, opposite in direction, and act on different objects (swimmer and wall).

Common errors and how to correct them

Confusing Newton’s first and third law. The first law is about a single object and its resultant force. The third law is about a pair of forces on two different objects.

Applying $F = ma$ using the total force instead of the resultant force. Always find the resultant force first, then substitute into $F = ma$.

Stating third-law pairs as “equal and opposite forces on the same object.” Third-law pairs always act on different objects. Equal and opposite forces on the same object produce equilibrium (Newton’s first law), which is a different concept.

How to apply this in an exam

For Newton’s second law questions, identify the resultant force before calculating. For Newton’s third law, always name both objects, both forces, and state the forces are equal, opposite, the same type, and act on different objects.