# GCSE Science/Newton's second law

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# Newton's Second Law[edit]

## Momentum[edit]

A motion of a body is described by its momentum. **Momentum** is the **product** of a body's **mass** and its **velocity**. Momentum has both *magnitude* and *direction*. Newton showed that **bodies only change their motion when a force is applied**, Newtons first law. The change in the momentum is equal to the applied force.

## Derivation of Newton's second law[edit]

Consider a snooker ball of mass *m* moving with a velocity *v*_{1}. The ball hits the cushion and bounces off, it now has a velocity *v*_{2}. The change in momentum is *mv*_{1} − *mv*_{2} = *m*(*v*_{1} − *v*_{2}).
The change in velocity is the acceleration, and so the change in momentum and hence force *F* is mass times acceleration, *F* = *ma*.
Thus Action and Reaction are equal but opposite in direction.