A single conservative force F(x) acts on a 3.2 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = -5.0xe-x/2 where x is in meters. At x = 5.0 m the particle has a kinetic energy of 3.0 J.
(a) What is the mechanical energy of the system?
(b) What is the maximum kinetic energy of the particle and
(c) the value of x at which it occurs?