Question

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.

Answer 1

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. \[1/2t^2(kv - 9.8) + Vot + Xo\]