A motorized drone moves horizontally at a constant speed \(v\) in an environment where the magnitude of the aerodynamic drag force on the drone is modeled by \(F_D = D v^2\), where \(D\) is a constant. The drone's motor delivers mechanical power \(P_0\) to maintain this speed. If the drone is instead operated to maintain a constant horizontal speed of \(2v\), how does the new mechanical power \(P\) delivered by the motor compare to \(P_0\), and what is the physical justification?