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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 t 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 c is a positive constant, and Newton’s Second Law gives
(a) Solve this as a linear equation to show that
(b) What is the limiting velocity?
(c) Find the distance the object has fallen after t seconds.
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Calculus, Early Transcendentals
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning