To stop instantly, you would need infinite deceleration. This in turn, requires infinite force, as demonstrable with this equation:F=maSo when you hit a wall, you do not instantly stop (e.g. the trunk of the car will still move because the car is getting crushed). In a case of a change in momentum, mv⃗ mv→, we can use the following equation to calculate force:F=p/hHowever, because the force is nowhere close to infinity, time will never tend to zero either, which means that you cannot come to an instantaneous stop.
