Impulse

Impulse measures how a force changes an object’s momentum when it acts for a certain time. It links force, time, and the change in motion during a push, hit, or collision.

Key Ideas

• Momentum: $p = mv$ (mass × velocity). It has direction.
• Impulse: force × time for which the force acts.
• Impulse changes momentum: same impulse means the same change in momentum.
• Units: newton–second (N s), which is the same as kg m s⁻¹.

Formulas you need:

$$J = F\,\Delta t = \Delta p$$$$\Delta p = m\,v_{\text{after}} - m\,v_{\text{before}}$$

If the force is not constant, the average force is $F_{\text{avg}} = \dfrac{J}{\Delta t} = \dfrac{\Delta p}{\Delta t}$.

How to Picture It

• Catching a ball: moving your hands backward increases the time $\Delta t$, so for the same change in momentum the average force on your hands is smaller.
• Car safety: airbags and crumple zones increase stopping time, reducing the force on passengers for the same impulse.
• Force–time graphs: the area under the graph equals impulse.

Common Misconceptions

• “Impulse is just force.” False—time matters. A small force acting longer can give the same impulse as a big force acting briefly.
• “Mass does not matter.” False—$\Delta p = m\,\Delta v$. Heavier objects need larger impulse for the same speed change.
• “Direction is not important.” False—momentum and impulse have direction. Use a positive direction and keep signs consistent.