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Air resistance acting on a falling body can be taken into account by the approximate relation for the acceleration: a= dv/dt = g  kv, where k is a constant. (a) Derive a formula for the velocity of the body as a function of time assuming it starts from rest (v=0 at t=0). [Hint: Change variables by setting u=gkv.] (b) Determine an expression for the terminal velocity, which is the maximum value the velocity reaches.
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