Newton's three laws of motion explained simply, with examples

This guide is for you if you want Newton’s laws to make sense, not just to memorise them. In CBSE they are taught in Class 9 in Force and Laws of Motion, and they return in Class 11 physics. They are also a core part of ICSE Class 9, GCSE and IGCSE physics. The laws are short, and once you can picture them, the calculations are straightforward.

The idea in plain words

A force is a push or a pull. It is measured in newtons (N).

When several forces act on an object, what matters is the resultant force (also called the net force or unbalanced force). If two forces are equal and opposite, they are balanced and the resultant force is zero.

Law	In one sentence	Everyday example
First law	An object stays still, or keeps moving at a steady speed in a straight line, unless a resultant force acts on it.	Passengers jerk forward when a bus brakes suddenly.
Second law	The resultant force equals mass times acceleration: F = ma.	A loaded trolley is harder to speed up than an empty one.
Third law	When object A pushes on object B, B pushes back on A with an equal and opposite force.	A rocket pushes gas backwards, and the gas pushes the rocket forwards.

First law: inertia

Objects resist changes to their motion. This property is called inertia, and the more mass an object has, the more inertia it has. If you are standing in a bus that brakes, your body tends to keep moving forward, which is why you lurch.

Second law: F = ma

• F is the resultant force in newtons (N)
• m is mass in kilograms (kg)
• a is acceleration in metres per second squared (m/s²)

One newton is the force that gives a 1 kg mass an acceleration of 1 m/s². CBSE also states the second law in terms of momentum: force is proportional to the rate of change of momentum. For a fixed mass, this gives F = ma.

You can rearrange it as a = F/m or m = F/a.

Third law: action and reaction

Forces always come in pairs. The two forces in a pair are equal in size, opposite in direction, the same type of force, and act on different objects.

Worked examples

Example 1: finding force

A car of mass 1,200 kg accelerates at 2.5 m/s². What resultant force acts on it?

1. F = ma
2. F = 1,200 × 2.5
3. F = 3,000

Answer: 3,000 N

Example 2: resultant force and acceleration

A box of mass 10 kg is pushed along the floor with a force of 50 N. Friction acts against it with a force of 20 N. Find the acceleration.

1. Find the resultant force: 50 - 20 = 30 N (in the direction of the push)
2. a = F/m = 30 ÷ 10
3. a = 3

Answer: 3 m/s²

Using 50 N instead of 30 N is a very common mistake. Always find the resultant force first.

Example 3: braking force

A car of mass 1,000 kg is moving at 20 m/s. The brakes bring it to rest in 4 s. Find the braking force.

1. Find the acceleration: a = (final velocity - initial velocity) ÷ time = (0 - 20) ÷ 4 = -5 m/s²
2. The minus sign shows the car is slowing down.
3. F = ma = 1,000 × (-5) = -5,000 N

Answer: a braking force of 5,000 N, acting opposite to the direction of motion.

Example 4: the third law in numbers

Two skaters stand on smooth ice. Skater A has a mass of 50 kg and skater B has a mass of 25 kg. A pushes B with a force of 100 N. Find the acceleration of each skater.

1. By the third law, B pushes A back with 100 N in the opposite direction.
2. Acceleration of A: a = 100 ÷ 50 = 2 m/s²
3. Acceleration of B: a = 100 ÷ 25 = 4 m/s²

Answer: A accelerates at 2 m/s² and B at 4 m/s², in opposite directions.

The forces are equal, but the lighter skater accelerates more. That is the second law and third law working together.

Common mistakes and how to avoid them

Thinking moving objects need a force to keep going. They need a force to change speed or direction, not to keep moving. On Earth, friction is the force that slows things down.

Using one force instead of the resultant. Draw a quick diagram with arrows, add forces in the same direction, subtract opposite ones, then use F = ma.

Saying action and reaction cancel. They act on different objects, so they never cancel each other.

Picking the wrong reaction pair. A book on a table: the pair to “Earth pulls book down” is “book pulls Earth up”, not “table pushes book up”. The table’s push is a different pair, between the book and the table.

Mass in grams. F = ma needs kilograms. 500 g is 0.5 kg.

Mixing up mass and weight. A 60 kg student has a weight of about 588 N on Earth (60 × 9.8). Mass is in kg, weight is a force in N.

Try these

1. Find the force needed to give a 5 kg mass an acceleration of 4 m/s².
2. A force of 600 N acts on a mass of 80 kg. Find the acceleration.
3. A 20 kg trolley is pushed with 120 N. Friction is 40 N. Find its acceleration.
4. A 1,500 kg car slows from 25 m/s to rest in 5 s. Find the braking force.
5. A book rests on a table. The Earth pulls the book down with its weight. What is the third-law pair of this force?

Answers

1. F = 5 × 4 = 20 N.
2. a = 600 ÷ 80 = 7.5 m/s².
3. Resultant = 120 - 40 = 80 N, so a = 80 ÷ 20 = 4 m/s².
4. a = (0 - 25) ÷ 5 = -5 m/s², so F = 1,500 × 5 = 7,500 N opposite to the motion.
5. The book pulls the Earth upwards with an equal force.

Still unsure?

If forces and motion still feel slippery, a Qlive teacher can work through them with you one-to-one, drawing force diagrams on the board in Qlive Space, starting with a free assessment that finds the exact gap. You can read more about how we teach on our physics page, and when you are ready for electricity, see our guide to Ohm’s law and circuits.