# Can such motion exist?

1. Sep 20, 2010

I know some people might think this topic is stupid but I am asking about it anyway.
Can any object real or theoretical move with a function x(t) where:
1_ x'(t) is undefined at all points
2_ x'(t) is an indeterminate form at one point
3_ x'(t) is defined at some points but undefined in others
4_ x'(t) have range of complex numbers
5_x'(t) approaches infinity
So can theoretical objects move with theoretical motion with such crazy velocities exists? if the velocity is infinity will an object exist in two places at the same time? can any real astronomic object move with such velocities because of effects of wormholes or black holes? Is it physically impossible within any universe for such motions to exist. If it isn't physically impossible is there a mathematical way to describe such motions?
I know I am asking about stupid stuff but it is just for curiosity.

2. Sep 21, 2010

The velocity is a smooth function F.A.P.P. (for all practical purposes) The mentioned artifacts can exist in limiting cases of physical toy models. They are not physical reality and never will be. Nature doesn't like divergences.
There are mathematical ways to describe such functions, but for these you need a deeper understanding of the types of derivatives that exist and the theory of measures.

3. Sep 21, 2010