A high-speed train travels at a constant velocity of \(50\text{ m/s}\) along a straight, horizontal track. At this speed, its engines deliver \(2.0\text{ MW}\) of mechanical power to overcome an aerodynamic drag force modeled by \(F_D = b v^2\), where \(b\) is a positive constant and \(v\) is the speed of the train. Assuming all other resistive forces are negligible, what mechanical power must the engines deliver for the train to maintain a constant velocity of \(100\text{ m/s}\)?