A falling object encounters air resistance that is proportional to its velocity. The
Chapter 6, Problem 42(choose chapter or problem)
Vertical Motion A falling object encounters air resistance that is proportional to its velocity. The acceleration due to gravity is -9.8 meters per second per second. The net change in velocity is dv/dt = kv - 9.8.
(a) Find the velocity of the object as a function of time if the initial velocity is \(v_{0}\).
(b) Use the result of part (a) to find the limit of the velocity as t approaches infinity.
(c) Integrate the velocity function found in part (a) to find the position function s.
Text Transcription:
v_0
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