A rocket burning its onboard fuel while moving through space has velocity v(t) and mass m(t) at time t. If the exhust gases escape with the velocity v sub e relative to the rocket, it can be deduced from Newton's Second Law of Motion:
m dv = dm v sub e
dt dt

a. show that v(t) = v(0) - ln(m(0)/m(t)) v sub e

b. For the rocket to accerate in a straight line from rest to twice the speed of its own exhust gases, what fraction of its intial mass would the rocket have to burn its fuel?

Any help would be greatly appreciated!!!!!!!!!! I really am not even sure where to start!!!