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>>Another mistake you make in your calculations is that you assume that the
>>exhausted mass and the exhaust velocity are constant at any time.
>>It's quite simple to see that that can't be true: The ship continues to
>>become lighter while it exhausts fuel therefore it also becomes easier to
>>accelerate. So for a constant mass exhaust and a constant exhaust velocity
>>you'll accelerate with an increasingly larger rate.
>Ah, no I included this in the total mass calculations.

Indeed you did include the fact that the ship became lighter, but not that
it would accelerate with a greater rate. You explicitly defined a=10 m/s/s
(Don't forget that 2nd /s otherwise your talking about velocity.)
The "t" in your formulas has a double meaning, which is why you confuse
yourself. The "t" in a(M + Mf * T - Mf * t) is an actual point in time,
while the "t" in (Mf * Vf) / t is actually a "dt", thus a per unit of time.

In short the relation m*a = (Mf * Vf)/t isn't valid if m changes during t.