A particle of mass m moves along the x-axis under the action of a force F(x)=−ax2, where a is a positive constant.
a. (i) Show whether or not this force is conservative.
b. (ii) Taking the potential energy to be zero at x=0, obtain an expression for the potential energy U(x) for the particle.
c. (iii) If the particle is released from rest at x=x0, derive an expression for its speed v when it reaches a general position x(0<x<x0).