Originally posted by AThousandYoung Let me try this again.
There is a little robotic space probe floating out in space that is not accelerating. We can take it's inertial frame of reference as v=0.
The engine, when on, provides 1 watt of power which is converted to kinetic energy. The probe has a mass of 2 kg. After one second, the probe has 1 J of kinetic energy, and it's veloc ...[text shortened]... to the probe's original velocity four seconds ago.
Why am I getting different answers?[/b]
An extremely intelligent person whom I shall call BrotherGeeWhiz commented on my confusion:
Power and Velocity. I think the issue would be resolved if you took into account the acceleration, which is the quantity I like to think about in classical mechanics. It's proportional to force and invariant to changes in inertial reference frames. If one proposes some continuous form for the acceleration, then the velocities should add along different reference frames (as long as v<<c).
Also (tiny point), for an isolated mass in space to move, it has to propel some "fuel" in the opposite direction to conserve momentum. This changes the mass, but since the fuel can move arbitrarily fast, the change in mass can be made arbitrarily small.