The position of a certain airplane during takeoff is given by \(x=\frac{1}{2} b t^{2}\), where \(b=2.0 \mathrm{~m} / \mathrm{s}^{2}\) and \(t=0\) corresponds to the instant at which the airplane's brakes are released at position \(x=0\). The empty but fueled airplane has an inertia of \(35,000 \mathrm{~kg}\), and the 150 people on board have an average inertia of \(65 \mathrm{~kg}\). What is the magnitude of the airplane's momentum \(15 \mathrm{~s}\) after the brakes are released?