On its takeoff roll, the airplane starts from rest and accelerates according to $a=a_{0}-k v^{2},$ where $a_{0}$ is the constant acceleration resulting from the engine thrust and $-k v^{2}$ is the acceleration due to aerodynamic drag. If $a_{0}=2 \mathrm{m} / \mathrm{s}^{2}, k=0.00004 \mathrm{m}^{-1}$
and $v$ is in meters per second, determine the design length of runway required for the airplane to reach the takeoff speed of $250 \mathrm{km} / \mathrm{h}$ if the drag term is $(a)$ excluded and
(b) included