When logic and calculus collide

[Kaizer007]

I'm sorry this is four days late, but I wanted to ask how the last part of Ken's argument way up there makes sense:

"a third assumption: that to speed up and slow down you must cross through the intermediate speeds - that you ramp up, and ramp down. True when speeding up, but if you run into a lamp post, brick wall, or parked car, your velocity instantly goes to zero. The graph of your velocity would have a discontinuity at that point, and would therefore be undefined (accelerated acceleration, or jerk). At that instant your velocity instantaniously goes from, lets say 12 mph, to 0."

I can't believe, (with only Physics and AP Physics class behind me *both High School Level*) that an instant stop is possible for running into a lamp post. I am to believe that even the slightest part of your body would start slowing down at a tremendous negative acceleration but not one that could be considered undefined. I had thought (from other math classes) that undefined acceleration could not be reached in this physical world.