Chapter 2, Problem 69P

(III) Air resistance acting on a falling body can be taken into аccount by the approximate relation for the acceleration:

$a=\frac{dv}{dt}=g-kv,$

where k is a constant, (a) Derive a formula for the velocity of the body as a function of time assuming it starts from rest (v = 0 at t = 0), [Hint: Change variables by setting (u = g − kv.]) (b) Determine an expression for the terminal velocity, which is the maximum value the velocity reaches.