Chapter 6, Problem 6.66CP

For t < 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed v_i. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: ${\stackrel{\to }{F}}_{\text{net}}=-mk{v}^2\hat{i}$, where k is a constant. The speed of the object after t = 0 is given by v = v_i/(1 + kv_it). (a) Find the position x of the object as a function of time. (b) Find the object’s velocity as a function of position.