1. The problem statement, all variables and given/known data A question asks to show for conservative forces,KE=f(v^2) and PE is independent of time. 2. Relevant equations 3. The attempt at a solution My attempts: from work energy theorem,increase in KE=work done =int F.dl=int m(dv/dt).(vdt) =(m/2) int d(v^2) Does this show kinetic energy is a quadratic function of v? Potential energy is a point function,i.e. it depends only on points.Once you get the value it will remain the same for all future instants...therefore potential energy does not depend on time. Please say if I am correct.