while deriving rocket equation we find change in momentum of rocket and this is the result: $$Δp=MΔV+Ve ΔM$$ from here we divide this by time to calculate force and since no external force(freespace) is acting we get: $A=Ve ΔM/M $ ($A $ is acceleration of rocket)
And now we integrate this with time to get change in velocity and we assume intial velocity is zero so we get real time velocity this is rocket equation. SO FAR EVERYTHING LOOKS CORRECT but in the equation : $Δp=MΔV+Ve ΔM$
since $ Δp=0$ and the equation becomes: $MΔV=-Ve ΔM$
dividing the whole by M we get:
this also tells change in velocity and since initial velocity is zero this will give me real time velocity but this is wrong I know because rocket equation is different what exactly is wrong with this thinking.