Using the assumption that air resistance is proportional to the square of the velocity of the falling dv kv? object, we can model the velocity of the falling object using the DE, Note that m is the dt mass of the object, g is the acceleration due to gravity, and k is a positive constant. Note also that for this application, we assume that the velocity v must be positive and in the downward direction. This means you can ignore the negative domain for v in your phase portrait below. a. Explain why this is an autonomous DE. b. Determine the terminal velocity of the falling object by finding any critical points of this DE and creating a phase portrait. Then sketch typical solution curves for v(t) on each region of the plane determined by the critical point(s) of this DE. Clearly label the formula for terminal velocity. In the phase portrait, label any equilibriums as stable, unstable, or semi-stable. Also show clear work to support your arrow directions on each interval on the v-axis phase line. (Don't use specific numbers for the constants! Keep these test values in terms of them.)