Is it possible for instantaneous acceleration magnitude to be infinite? For example if we happen to take 2 blocks of mass 1 kg each and place them on a frictionless surface. If we project 1 block at the other at some velocity v, assuming the collision is perfectly elastic, the second block will absorb all the momentum of the first and start moving with velocity v.
Now if we look at the point in time where the 2 blocks came in contact, then the acceleration at this point will be dv by dt. At this point, velocity was 0 at the precise moment the blocks touched and velocity was v at time dt later. Using the limit definition of derivative, the acceleration is v minus 0 by dt when dt approaches 0. This should in fact return the answer as infinity.
This may be considered 'aphysical' per se but even with not totally elastic collision and friction etc, it should still return acceleration as infinity.
So ame I somehow wrong or can acceleration be infinite in a point in time. I am not asking whether ANY acceleration is possible in 1 d space rather I am asking if infinite acceleration is possible in general and if not, I ask for justification against the example i used.
