An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s (t) is the distance dropped after seconds, then the speed is v = s’ (t) and the acceleration is a = v’ (t). If g is the acceleration due to gravity, then the downward force on the object is mg = cv, where is a positive constant, and Newton’s Second Law gives m dv/dt = mg - cv
(a) Solve this as a linear equation to show that v = mg / c (1 – e–ct/m).
(b) What is the limiting velocity?
(c) Find the distance the object has fallen after seconds.