A single conservative force F(x) acts on a 1.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by where x is in meters. At x = 5.0 m the particle has a kinetic energy of 2.0 J.

(a) What is the mechanical energy of the system?

(b) Make a plot of U(x) as a function of x for 0 < x < 10 m, and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine

(c) The least value of x the particle can reach and

(d) The greatest value of x the particle can reach. Use part (b) to determine

(e) The maximum kinetic energy of the particle and

(f) The value of x at which it occurs.

(g) Determine an expression in Newton’s and meters for F(x) as a function of x.

(h) For what (finite) value of x does F(x) = 0?