A single conservative force F(x) acts on a 2.9 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = -3.8xe^-x/5 where x is in meters. At x = 4.5 m the particle has a kinetic energy of 12 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?