What is the formula for variable mass systems and rockets?

[UchihaClan13]

Okay guys
I am studying variable mass systems and rockets,as such
I was introduced to the formula v=u*ln M₀/M
where v is the velocity of the rocket after a time t
M₀is the initial mass of the rocket,M is the mass of the rocket after time t
u is the velocity of the ejected gas w.r.t to the rocket
The mass is being lost(in the form of fuel being used up to propel the rocket and provide it the required upward force) at a constant rate r=-dM/dt
Could any of you guys help me with the derivation of this "useful" equation?
I just started learning integration
Hence i can't figure out the integrand so easily
Thanks in advance!:)
UchihaClan13

 

[jtbell]

Could any of you guys help me with the derivation of this "useful" equation?

If you give us a link to a specific derivation and tell us exactly where you get "stuck", someone can probably help you.

 

[UchihaClan13]

Okay I will
Thank you:)