Don't know if this is the correct place to post this, this is not an assignment question, but I am terribly stuck with this. While going through the derivation of contact time for a hertzian contact as given in problem 3 at the following link http://s17.postimg.org/t1kq6mlxr/Capture.png , I am not able to understand how the integral form for contact time has come into picture. I understand that the twice the integral of displacement over velocity from x=0 to x=x0 gives the total contact time. But can anyone please explain the in-between steps to get the same (how did the 1/sqrt(1-(x/x0)^5/2) come about? I understand that this is a very trivial problem but it will be a great help to understand the steps.