Ya but realise that both the proton and the electron start moving. The motion as such is not really simple as the accelerations are different and the acceleration at any instant depends on the distance between the two. I found it tough to correlate all this. By the way the solution given in the study material in which I came across this problem conviniently ignored the K.E. of the proton and arrived at an answer. I am not sure if that was meant to be an approximation, neither do I know if the approximation is valid if done.