A particle of mass m travels on the positive x axis, beneath the influence of the conservative force with potential energy
V(x) =V0 e−αx.
(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: Utilize conservation of energy to get an equation for dx/dt.)
(iii) Compute the time when ax = 1.0