In an experiment, one of the forces exerted on a proton is F with arrow = -ax2i, where a = 11.4 N/m2.

(a) How much work does F with arrow do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)?

(b) Along the straight-line path from the point (0.11 m, 0) to the point (0.31 m, 0)?

(c) Along the straight-line path from the point (0.31 m, 0) to the point (0.11 m, 0)?

(d) Is the force F with arrow conservative?Yes or no? Explain.

(E) If F is conservative, what is the potential-energy function for it? Let U = 0 when x = 0. (Use the following as necessary: x and a. Do not substitute numerical values; use variables only. If F is not conservative, enter NC.)