A rocket is moving with constant acceleration 6. Assume external forces on it to be zero. Exhaust gases escape with velocity u relative to the rocket. Find how its mass changes with time if its initial mass is `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