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An Object with Mass mm Is Dropped from Rest and We Assume That the Air

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An object with mass mm is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t)s ( t ) is the distance dropped after tt seconds, then the speed is v=s(t)v = s ^ { \prime } ( t ) and the acceleration is a=v(t)a = v ^ { \prime } ( t ) . If gg is the acceleration due to gravity, then the downward force on the object is mgcvm g - c v , where cc is a positive constant, and Newton's Second Law gives mdvdt=mgcvm \frac { d v } { d t } = m g - c v . Find the limiting velocity.

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