Newton's laws of motion

The three laws

1. A body stays at rest or moves with constant velocity unless a resultant force acts on it.

2. F = ma: resultant force (N) = mass (kg) × acceleration (m/s²), in the direction of the acceleration.

3. If A exerts a force on B, then B exerts an equal and opposite force on A.

Forces you meet

• Weight W = mg, acting vertically down.
• Normal reaction R, perpendicular to a surface.
• Tension in a string (pulls) or thrust in a rod (pushes).
• Friction and resistance, opposing motion.
• Driving force from an engine.

Method

1. Draw a force diagram and mark the acceleration with a separate arrow.

2. Resolve perpendicular to the motion: these forces balance (no acceleration that way).

3. Resolve along the motion: resultant force = ma.

Worked example

A car of mass 1200 kg has a driving force of 3000 N and meets a resistance of 600 N. Find its acceleration.

1. Resultant force = 3000 - 600 = 2400 N.
2. 2400 = 1200a.

Answer: a = 2 m/s²

Check yourself

1. A van of mass 1500 kg has a driving force of 2400 N and a resistance of 900 N. Find its acceleration.
   Show answer

   1 m/s². 1500 = 1500a, so a = 1 m/s².

2. A particle of mass 2 kg is pulled vertically upwards by a string with tension 30 N. Find its acceleration, to 2 significant figures.
   Show answer

   5.2 m/s². 30 - 2(9.8) = 2a, so a = 5.2 m/s².

3. A box of mass 4 kg on a smooth horizontal floor is pulled by a force of 20 N at 30° above the horizontal. Find its acceleration, to 3 significant figures.
   Show answer

   4.33 m/s². 20 cos 30° = 4a, so a = 4.33 m/s².

4. For the same box (4 kg, 20 N at 30° above the horizontal), find the normal reaction from the floor, to 3 significant figures.
   Show answer

   29.2 N. Vertically: R + 20 sin 30° = 4g, so R = 39.2 - 10 = 29.2 N.

5. A resultant force of 45 N gives a particle an acceleration of 3.6 m/s². Find its mass.
   Show answer

   12.5 kg. m = F/a = 45/3.6 = 12.5 kg.

6. A book rests on a table. By Newton's third law, which force pairs with the weight of the book (the Earth pulling the book down)?
   • The table pushing the book up
   • The book pulling the Earth up
   • The book pushing the table down
   • Friction on the book
   Show answer

   The book pulling the Earth up. Third-law pairs act on different bodies and are the same type of force: the Earth pulls the book, so the book pulls the Earth.

7. A particle moves with constant velocity. What is the resultant force on it?
   • Equal to its weight
   • In the direction of motion
   • Opposite to the motion
   • Zero
   Show answer

   Zero. Newton's first law: constant velocity means no resultant force.

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Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit M1
• Pearson Edexcel IAL Mechanics M1 (WME01) question paper, January 2024: front-cover instructions on g and accuracy

Last updated 7 November 2026. Spotted a mistake? Tell us.