3. A particle of mass m = 3 kg has the potential energy function U(x)=3(x-1)-(x-3)³ where x is measured in meters and U in joules. The following graph is a sketch of this potential energy function. Energy U(x) E- E₁- E₁- x X₂ The energies indicated on the vertical axis are evenly spaced; that is, E,-E, E,-E,. The energy E, is equal to U(x,), and the energy E, is equal to L(x). (a) Determine the numerical values of x, and x,. (b) Describe the motion of the particle if its total energy is E (c) What is the particle's speed at x = x, if its total energy, E, equals 58 J? (d) Sketch the graph of the particle's acceleration as a function of x. Be sure to indicate x, and x, on your graph. (e) The particle is released from rest at x=x,. Find its speed as it passes through x = x. 4. The force on a 6 kg object is given by the equation: F(x)=3x+5, in newtons. The object is moving 2 m/s at the origin. (a) Determine the work done on the object by the force when it is moved 4 m from the origin in the x direction. (b) Determine the speed of the object when it has moved 4 meters.