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?

P = F V
P = m a v  (M = 1, P = 1)
1 = a v
1 = dv/dt v
dt = v dv
t = 1/2 v^2
2t = v^2
v = (2t)^.5
a = dv/dt
a = (2t)^(-0.5)