A ball of mass m is dropped from rest. Let s(t) be the distance that ball traveled after t seconds. Then v(t) = s 0 (t) is the speed and a(t) = v 0 (t) is the acceleration of the ball. We assume that the air resistance is proportional to the speed of the ball. If g is the acceleration due to gravity, then the downward force on the object is mg − cv, where c is a positive constant. The Newton Second Law then gives mv0 = mg − cv.

(1) Solve the above linear differential equation to find the velocity v(t).
(2) What is the limiting velocity of the ball as t → [infinity]?
(3) Find the distance the ball has traveled after t seconds