Do I need to integrate twice for calculating velocity in Kerbal Space Program?

[iknowsigularity]

So i was playing Kerbal Space Program and decided i wanted to calculate the maximum velocity of my ship. First, I formed this equation. A(t) = M - dm/dt (t) Where A is the amount of fuel at a given time, M is the total mass of the fuel, Dm/dt is the rate of change of the mass of the fuel, and t is time. As far as experiments in game show this equation works. The problem occurs when i want to calculate the maximum velocity. First i differentiated F = MA and solved for da/dt which gave me -F(dm/dt)/m^2 = da/dt. This gives me the jerk and i believe by multiplying it by t I can get the acceleration at a given time. (-F(dm/dt)/m^2 )(t) = a(t) .
From here I'm stuck. I can conceptualize how to obtain the velocity from this point. I started thinking of summation and that lead me take the integral. So my question is could I get the velocity at a given time by integrating this equation (-F(dm/dt)/m^2 )(t) = a(t)? Not sure if i provided enough information but thanks to anyone who can help.

 

[Dr. Courtney]

Yes, you need to integrate. One approach is described in the linked paper:

http://arxiv.org/ftp/arxiv/papers/0903/0903.1555.pdf

 

[iknowsigularity]

Yes, you need to integrate. One approach is described in the linked paper:

http://arxiv.org/ftp/arxiv/papers/0903/0903.1555.pdf

thank you!

 

[iknowsigularity]

Yes, you need to integrate. One approach is described in the linked paper:

http://arxiv.org/ftp/arxiv/papers/0903/0903.1555.pdf

I actually have one more question. Would I need to integrate twice to go from jerk to acceleration then from acceleration to velocity or could I just take the integral of the equation I posted of acceleration as a function of time. Still reading through paper it might answer this.