A rocket firing its engine and accelerating in outer space (no gravity, no air resistance) suddenly runs out of fuel. Which best describes its motion after burnout?

A. It continues to accelerate but at a gradually decreasing rate, until it reaches a constant velocity.

B. It continues to accelerate at the same rate.

C. It immediately begins slowing down and gradually approaches zero velocity.

D. It immediately stops accelerating, and continues moving at the velocity it had when burnout occurred.

the correct choice is

D. It immediately stops accelerating, and continues moving at the velocity it had when burnout occurred.

as soon as the rocket runs out of fuel, its engine stops firing gases which is mainly responsible for the acceleration of the rocket. hence the rocket stops accelerating. also, since there is no gravity or air resistance, there is no net force on the rocket after it runs out of the fuel. hence

a = acceleration = 0

we know that, at no acceleration, object moves at constant velocity. hence the rocket keeps moving at the velocity it had when burnout occured.