From force to impulse
Start again from \vec{F}_{\text{net}} = d\vec{p}/dt and just multiply both sides by a slice of time dt, then add up all the slices during which the force acts. The total is the change in momentum. We call this accumulated "force times time" the impulse, written \vec{J}.
The impulse-momentum theorem: the impulse of the net force equals the change in momentum it produces. Its unit, the newton-second (N·s), is identical to kg·m/s.
This is the impulse-momentum theorem, and it is genuinely useful because it lets you skip the messy instant-by-instant details of a force. You do not need to know how the force spikes and fades during a collision; you only need the total impulse, and that tells you exactly how much the momentum changed.
When the force is constant (or when you use its average value), the integral becomes a simple product. This is the form you will reach for most often.
For a constant or average force, impulse is force times contact time. Graphically, impulse is the area under a force-versus-time curve.
The airbag principle
Now read the theorem sideways. Suppose the change in momentum is fixed — a car and its passenger must go from highway speed to a dead stop, so \Delta p is settled no matter what. The theorem then says F_{\text{avg}}\,\Delta t is fixed. If you can stretch out the time \Delta t, the average force must shrink in proportion. That is the entire secret of the airbag: it lengthens the stopping time from milliseconds to tens of milliseconds, cutting the peak force on your body by the same factor.