A particle of mass m moves on the positive x axis, under the influence of a cons

Question

A particle of mass m moves on the positive x axis, under the influence of a conservative force with potential energy
V(x) = V0 e??x.
(A) Describe the force in words.
(B) Suppose the initial position is x=0 and the initial velocity is v=0, at time t=0. Determine the position x(t) as a function of time. Show your work. (Hint: Use conservation of energy to derive an equation for dx/dt.)
(C) Calculate the time when ?x = 1.0.
(D) By hand, sketch a qualitatively accurate graph of x versus t. Use graph paper. Label the axes. Put the point from (C) on the graph.

Explanation / Answer

V(x) = Vo*e^(??x). F = -V'(x) = Vo*e^(??x).

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