potential = 0 particle of mass m charge q is projected with kinetic energy K at a nucleus mass M charge Q that is at rest. it is shot with 'perfect aim' (along the x axis). find the distance x to the nucleus when dx/dt of particle is zero. i know that F = dK/dt = cqQ/x^2 where c = 1/4pi(epsillon naught) .5m(d/dt)v^2 = cqQ/x^2 (1) the coulomb force is position dependent force, so: .5m(dv^2/dx)(dx/dt) = cqQ/x^2 (2) .5m(dv^3) = cqQ(dx/x^2) (3) this doesn't make any sense to me. it makes more sense to take the time derivative in (1) just giving Newtons 2nd, and then doing the position dependence. ma = cqQ/x^2 mvdv = cqQ(dx/x^2) .5mv^2 = -cqQ/x and then ????? i got nothing. any suggestions, clarifications or anything of the like would be much appreciated.