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 If m = 1000 kg, F = 50,000 N, D = 2000 v, and g = 9.81 m/s2, find the time...

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

If
m
= 1000 kg,
F
= 50,000 N,
D
= 2000
v, and
g
= 9.81 m/s², find the time variation of the velocity of the rocket,

using the initial conditions
x(0) = 0 and
v(0) = 0, where
x(t) is the distance traveled by the rocket in time
t.