We know that, with gravity for example, that ma = GmM/r^2. For simplicity's sake and the sake of my question, let us say that a=c/r^2, where c is GM. Basically, I am wondering how I can use this to create the most accurate displacement equations possible. My problem, however, is that a is dv/dt...or dx^2/dt^2, but I doubt you can do dx^2/r=cdt^2 and integrate twice or whatnot. Does anyone have some clarity? I have though to do a=c/(r-x)^2, where r is the initial distance and x is the distance traveled, but that still yields nothing helpful.