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**A solid fuel rocket, home constructed, has initial mass 10 kg; this, fuel is 8 kg. The rocket is launched vertically, from rest; burning the fuel at a constant rate equal to 0.225 kg/s, ejecting the exhaustion gases at a speed of 1980 m/s in relation to the rocket. Assume that the outlet pressure is the atmospheric and that the air resistance can be neglected. Calculate the velocity of the rocket 20 seconds after the launch and the distance traveled in the same interval.**

I tried to find the velocity through the integral equation of the conservation of mass, but I do not have the areas. I could assume that they simplify, although I am not sure how to deal with the specific mass or volume, since they vary. I imagine that the values will come by through some ODE.

Thanks, in advance.