This is an interesting problem, but not that interesting, really. The really interesting problem is an ant walking on the surface of an expanding sphere, where

This is an interesting problem, but not that interesting, really. The really interesting problem is an ant walking on the surface of an expanding sphere, where the rate of the expansion of the sphere is proportional to the radius of the sphere. If the ant starts at one pole, will it ever reach the other pole? Yes, I've underspecified the problem - we want the complete set of solutions. Assume initial radius r, ant of length l, ant walking at speed w, and initial rate of expansion e (remembering that de/dt is proportional to r). Under what conditions will an ant at pole P1 reach P2? Under what conditions is impossible for the ant to reach P2? Presumably there is a range of values such that the ant can traverse the sphere if it starts early enough or is big enough or if w is high enough. Now make things even more interesting: Assume that there is a maximum speed M, and that the closer w or e gets to M, the harder it is to get incrementally close to M. This is the expanding universe. We are the ant. If we had developed high speed interstellar travel "early enough", would we ever have been able to cross the universe? Or is it always too late? Now that's an interesting problem. Solution left as an exercise for the reader.