The differential equation governing the velocity v of a falling mass m subjected to air...

The differential equation governing the velocity v of a falling mass m subjected to air resistance proportional to the instantaneous velocity is

Where k is a positive constant of proportionality.

(a) Solve the equation subject to the initial condition

(b) Determine the limiting, or terminal, velocity of the weight.

(c) If distance s is related to velocity find an explicit expression for s if it is further known that