Answer:
It immediately stops accelerating, and continues moving at the velocity it had when the burnout occured.
Explanation:
Since the firing Engine of rocket will provide sufficient force to accelerate the rocket
Since the fuel of the rocket is burnt out so there is no source of energy remains in the rocket which will accelerate it to higher velocity
Also it is given that there is no air resistance or no gravity on the rocket in outer space
So immediately after the fuel is burnt the force on rocket will become zero and hence its acceleration will be zero
So correct answer will be
It immediately stops accelerating, and continues moving at the velocity it had when the burnout occured.