Space mag lev.

There is a 1 kilogram mag lev train in space that propels itself by converting 1 joule of electric energy into kinetic energy per second. There is no resistance and the train's mass remains constant during the experiment. What is it's acceleration?

Why doesn't the train accelerate at double the rate it did when it was expending 1 joule per second?
Because the acceleration of the train is not directly proportional to the power expended. Start with this:

K = mv^2/2

The question gives us power, so differentiate with respect to t:

dK/dt = m*2v*(dv/dt)/2
P = mva
a = P/mv

And there's your answer. The question does not give the current velocity of the train, so we can't figure out its acceleration.