as The equation of motion of a particle under the action of a position dependent force is given F(x)=m- dx dt (a) Prove that the change in the kinetic energy is equal to the work done by the force as the particle moves from an initial position x (at time to ) to a position x (at a later time t), that is K-K = *F(x)dx = W (b) Assuming that the particle moves in a system, show that such a position dependent forces is conservative. (c) When such forces are conservative show that one can define a potential energy function associated with that force such that F(x): =- Also prove that mechanical energy E is conserved; that is K+V=E= constant. dV (x) dx