In Section 1 3 we saw that the autonomous differential equation dv m mg kv dt where k is a positive constant and g is the

Question

In Section 1 3 we saw that the autonomous differential equation dv m mg kv dt where k is a positive constant and g is the acceleration due to gravity is a model for the velocity v of a body of mass m that is falling under the influence of gravity Because the term kv represents air resistance the velocity of a body falling from a great height does not increase without bound as time t increases Use a phase portrait of the differential equation to find the limiting or terminal velocity of the body lim v t48 Explain your reasoning O The phase portrait indicates that the terminal velocity is an asymptotically stable critical point The phase portrait indicates that the terminal velocity is egative infinity since the velocity decreases for all time The phase portrait indicates that the terminal velocity is an unstable critical point The phase portrait indicates that the terminal velocity is infinity since the velocity increases for all time The phase portrait indicates that the terminal velocity is a semi stable critical point

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