For t < 0, an object of mass m experiences no force and moves in the positive x

Question

For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: net = ?mkv2, where k is a constant. The speed of the object after t = 0 is given by
v = vi/(1 + kvit).
(a) Find the position x of the object as a function of time. (Use the following as necessary: k, m, t, and vi.)
x(t) =

(b) Find the object's velocity as a function of position. (Use the following as necessary: k, m, t, vi, and x.)
v(x) =

Explanation / Answer

x(t) = vi x ln(1 + kvit)/ kvi

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