Why would'nt this work?
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Move a sheet up and down rapidly
You can see the wave travel across it
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Everything soft and slow like your brain yes.
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Your push would travel at the speed of sound in the stick. You could think of hitting a pipe with a hammer, the sound of the hit would travel at the speed of sound, same is true for you pushing the stick.
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Well, it made me feel smart. So either you're a good teacher, and helped me put into words and solidify something I already understood more abstractly. Or you're a terrible teacher, and have led me further astray.
Pretty rough dichotomy there. I would not want to be an educator.
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The punching-through should start at the point of impact, since that end of the pole and that spot on the wall pole both know about the collision at that moment, and then the information travels back through the pole. So I think the front end of the pole would start breaking through the wall immediately, while the information about the impact is still traveling back through the pole. For that reason I think the front end of the pole might end up sticking farther out of the barn than the back end, because it has more time to so it. Would be interesting math, which I've never tried to figure out.
There can't be infinite deceleration, for the same reason that the back end of the pole can't instantly know the front end has run into the wall. Deceleration travels back through the length of the pole as its atoms squish up against the atoms in front of them and slow down.
Interesting for sure!