Question: A model for the velocity of a falling object with mass m is the differential equation dv dt Acceleration due to gravity is g

A model for the velocity of a falling object with mass m

A model for the velocity of a falling object with mass m is the differential equation dv dt Acceleration due to gravity is g > 0 and k k (v + mg) === m k 0 is the air resistance coefficient. (a) Find and classify equilibrium points using a phase line. (b) Sketch solution curves based on your phase line. (c) Use separation of variables and find the solution satisfying the initial condition v(0) = 0. (d) Evaluate and interpret lim v(t). 8047 (e) How long will it take for the velocity of the falling object to reach -mg/2k?

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