Say you're given a function that represents the kinetic energy of some object, what would you have to do to derive the force from that function? I know that for motion along a straight line a conservative force F(x) is the negative derivative of its associated potential energy function U, but what is there to do if the function is one of kinetic energy?
Conservation of energy and the work-energy relation will be useful in such cases. You usually will need more information than kinetic energy with position alone. Do you have an example. Note: For a conservative field, the force on an object at a position is the negative gradient of the potential energy function at that position. Motion does not have to be along a straight line.