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Hi all,

I'm posting here because I see an apparent paradox between what intuition and equations tell me. I'm sure it's a question of referential or something like that, but I just can't see it clearly...

So it's all about power and acceleration. Suppose the following situation : consider a spaceship under constant acceleration. Let's say it's a fictionary reactionless propulsion and not bother about fuel depletion, efficiency or other topics : ship mass stays constant, all energy is used for propulsion, there is no friction at all and we do not reach relativistic speeds.

Intuitively, you will say that this ship would use for its propulsion a constant power output. Thrust is the same at all time, forces and the physical mechanism that produce them are the same, so power output should be the same. Intuitively, a ship with a given power unit should be able to sustain constant acceleration infinitely, given we take out the fuel, efficiency and other problems.

But equations say that power depends on time as speed must be considered to compute the link between power and acceleration. They say P=m.a^2.t and so says the unit check : W=kg.m.s^-3, which is consistent with the formula.

It's been 15 years since I've not taken to this kind of physics problems, now I tangle only with IT problems, and so I fear I'm a little rusty by now. I'm sure the answer is simple, but I've lost something essential in my reasoning... Thanks for any hint to find it back ^-^

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# Power and Acceleration

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