The equation of motion of a rocket, of mass \(m\), traveling vertically under a thrust \(F\) and air resistance or drag \(D\) is given by

\[m \dot{u}=F-D-m g\]

If \(m=1000 \mathrm{~kg}, F=50,000 \mathrm{~N}, D=2000 \mathrm{v}\), and \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\), find the time variation of the velocity of the rocket, \(u(t)=\frac{d x(t)}{d t}\), using the initial conditions \(x(0)=0\) and \(v(0)=0\), where \(x(t)\) is the distance traveled by the rocket in time \(t\).