# Is there such a thing as instantly stopping?

I'm sorry if this is a stupid question, but I've never taken a physics class and I was curious about something. But anyway, my question is, is there such a thing as instantly stopping? For example, if I'm traveling at 70MPH and I hit a wall, between the time that I am going at full speed and when I hit the wall, do I slow down until I reach zero, or do I instantly stop? Do I go every speed in between 70 and 0?

To stop instantly, you would need infinite deceleration. This in turn, requires infinite force, as demonstrable with this equation: $$\vec F=m\vec a$$ So 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, $m\vec v$, we can use the following equation to calculate force: $$F=\frac{\Delta{p}}{\Delta{t}}$$ However, 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.