Physics
Basic

Newton's Second Law

Force equals mass times acceleration.

Formula

F=maF = ma

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Variables

FForce (N)
mMass (kg)
aAcceleration (m/s²)

Example

A 2 kg cart pushed with 10 N accelerates at a = 10/2 = 5 m/s².

How it works

Newton’s Second Law tells you how a force changes an object’s motion: the more net force you apply, the more its speed or direction changes. It also shows that mass matters, because the same force produces less acceleration on a heavier object. This relationship works because force is the cause and acceleration is the effect, so measuring both lets you predict motion quantitatively.

When to use it

Use this when you know the net force on an object and want to find its acceleration, or when you know the mass and acceleration and need the force. It is common in mechanics problems involving pushing, pulling, lifting, braking, and any situation where motion changes under a net force.

Worked example, step by step

A 6 kg sled is pulled with a net force of 18 N. Use Newton’s Second Law: F = ma Rearrange to find acceleration: a = F / m Substitute the values: a = 18 / 6 Calculate: a = 3 m/s² Final answer: the sled accelerates at 3 m/s².

Common mistakes to avoid

  • using total force instead of net force
  • mixing up mass and weight
  • forgetting to keep units in kilograms, newtons, and m/s²

Did You Know?

F = ma is the equation on which all of classical mechanics is built — Newton wrote it in his 1687 Principia.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026