The following equation describes the motion of a rocket that is expelling a total mass M of fuel at a rate α = -dm/dt: dv/dt = uα/(M-αt), where u is the speed the fuel is ejected, v is the velocity of the rocket in the x-direction, and t is time. Assume the velocity at t = 0 is v(0) = 0, and that M, u, and α are constants. A particular rocket burns fuel at a rate of 5.7 kg/sec with a propellant speed of 5.99 m/sec. The total mass of fuel is 133.1 kg. What is the speed (m/s) of the rocket at t = 2.8 sec? At what time (s) will the rocket run out of fuel and no longer be accelerating? Assume negligible rocket body mass

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