Question: If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is

If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is

where t is the acceleration due to gravity and c is a positive constant. (In Chapter 9 we will be able to deduce this equation from the assumption that the air resistance is proportional to the speed of the object; c is the proportionality constant.)
(a) Calculate limt _{t→ ∞} v. What is the meaning of this limit?
(b) For fixed t, use 1’Hospital’s Rule to calculate lim _{c → 0} + v. What can you conclude about the velocity of a falling object in a vacuum?

-et/m - (1 e ct/m mg

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