• anonymous
i'm hoping someone can help me with this problem.. A falling object encounters air resistance that is proportional to its velocity. The acceleration due to gravity is -9.8 m/s. 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 Vo 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.
  • Stacey Warren - Expert
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  • jamiebookeater
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  • anonymous
For a, if you integrate with respect to t you will get your velocity function v(t) = kvt - 9.8t + Vo Because v(t) is a polynomial to take the limit as t approaches infinity just plug in infinity and use l'hopitals rule to evaluate since it is a indeterminate form c. \[1/2t^2(kv - 9.8) + Vot + Xo\]

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