On its takeoff roll, the airplane starts from rest and accelerates according to a = a0 –...

On its takeoff roll, the airplane starts from rest and accelerates according to a = a₀ – kv², where a₀ is the constant acceleration resulting from the engine thrust and –kv² is the acceleration due to aerodynamic drag. If a₀ = 2 m/s², k = 0.00004 m^-1, and v is in meters per second, determine the design length of runway required for the airplane to reach the takeoff speed of 250 km/h if the drag term is (a) excluded and (b) included.