Find the mass of the rocket as a function of time, if it moves with a constant acceleration `a`, in absence of external forces. The gas escapes with a constant velocity `u` relative to the rocket and its mass initially was `m_0`.

Explanation

`F = (d)/(dt) (-Mu) = -u(dM)/(dt)` ( since u is constant )
`:. M omega = -u (dM)/(dt)` ( where ` omega` is its acceleration )
`(dM)/(M) =(-d omega)/( u)`
Integrating log `M=-(omega)/(u)t+C`
when t=0 , `M=M_0`
so ` C= log M_0 , log M = -(omega)/(u) t + log M_0 :. log (M)/(M_0) = -(omega)/(u) t`
` (M)/(M_0)=e^((omega)/(u)t) or M = M_0e^((omega)/(u)t)`
Thus , the mass of the rocket changes exponentially