Dickfore,
Thanks, but the question was about U. I didn't ask how to solve this problem. :) Anyway the approach using the law of conservation of energy leads to 1st order ODE instead of 2 order ODE for equation of motion. This is good.
K^2 Of course, it is a fiction problem. I should wrote...
At a certain distance in vacuum there are proton and electron (they are at rest with resptect to their's CM). I wonder after what time will they collide?
Of course, we neglect the fact that when the distance between the particles become very small, there is not only an electrical force acting...