A particle of mass m moves on the positive x-axis, beneath the influence of a conservative force having potential energy:
V(x) = V0 e-ax.
(i) Explain the force in words.
(ii) Assume that the initial position is x = 0 and the initial velocity is v = 0, at time t = 0. Find out the position x (t) as a function of time. Show your work. (Hint: Employ conservation of energy to derive the equation for dx/dt.)
(iii) Compute the time when ax = 1.0.