1. (25pts.) Consider the potential energy graph for a particle constrained to one dimensional motion along the x-axis. Distance is measured in units of a and energy is measured in units of Eo, i.e., each horizontal division has a magnitude of a meters, and each vertical division has a magnitude of Eo joules. (.) HE x (a) (a) In the figure, locate the equilibrium points and specify if they are stable or unstable. Explain. (b) Determine in which interval(s) is the force pointing to the right, and in which interval(s) is the force pointing to the left. (c) For the case when the particle has a mechanical energy equal to 10Eo, answer the follow- ing questions: i. In what region(s) is the particle allowed to move? Explain. ii. At what point(s) is the speed of the particle maximum and at what point(s) is it minimum? Explain. (d) Repeat part (c) for the cases where the mechanical energy of the particle is 4E0, -2E0, and -4E0.