Calculating change in momentum (HT ONLY)

Calculations involving conservation of momentum can be solved by calculating the total momentum before and after an event and equating them.
- If two objects are travelling in the same direction, their momentums are added.
- If two objects are travelling in opposite directions, then their momentums are subtracted.

Combining the equations \(F=ma\) and \(a=\dfrac{\Delta v}{t}\) leads to the relation between force and momentum: \(F=\dfrac{m\Delta v}{t}\). This equation shows that force is equal to the rate of change of momentum.
To stop moving, a force must be applied to change momentum to zero. Increasing the time it takes to stop will reduce the rate of change of momentum and the force. This principle is applied in numerous safety features such as crash mats and other cushioned surfaces, helmets, shin pads and other protective gear, seat belts and airbags in cars, and crumple zones, which collapse during a collision.

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