When we​ cough, the trachea​ (windpipe) contracts to increase the velocity of the air going out. This raises the questio

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When we​ cough, thetrachea​ (windpipe) contracts to increase the velocity ofthe air going out. This raises the question of how much it shouldcontract to maximize the velocity and whether it really contractsthat much when we cough.
Under reasonable assumptions about the elasticity of thetracheal wall and about how the air near the wall is slowed byfriction, the average flow velocity v can be modeled by theequation below, where ro is the resting radiusof the trachea in centimeters, r is the radius of the trachea and cis a positive constant whose value depends in part on the length ofthe trachea. Given the function below, complete parts a and bbelow.
v(r)= c(r0 - r)r2 cm/s, wherer0 /2 < r < r0.