An object of mass m is released from rest in a medium in which the frictional forces are...

An object of mass m is released from rest in a medium in which the frictional forces are proportional to the square of the velocity. The initial-value problem that governs the subsequent motion is

where v(t) denotes the velocity of the object at time t , y(t) denotes the distance traveled by the object at time t as measured from the point at which the object was released, and k is a positive constant.

(a) Solve (1.12.6) and show that

(b) Make a sketch of v2 as a function of y.