Final answer:
The change in a rocket's velocity when its mass decreases due to fuel burn is impacted by conservation of momentum and Newton's third law. As the rocket mass decreases, the acceleration increases since less mass is being acted upon by the force of the ejected fuel, which changes the velocity of the rocket.
Step-by-step explanation:
The question concerns the change in velocity of a rocket as it burns fuel and ejects it as exhaust in space. The important physical principle at work here is the conservation of momentum, which states that the momentum of a closed system remains constant if no external forces act on it. Since the rocket is in deep space, it can be considered a closed system with no external forces. As the rocket burns its fuel, the mass decreases (noted as dmg), causing an increase in the rocket's velocity (notated as dui). This change in the rocket's momentum due to varying mass keeps the total momentum conserved, which answers the question about how the rocket could slow down but not stop as a result of firing the engines and expelling fuel.
When the rocket ejects fuel, the force exerted on the escaping gas results in an equal and opposite force on the rocket. This is due to Newton's third law of motion, which tells us that every action has an equal and opposite reaction. However, the actual velocity change of the rocket will not be linearly dependent on the mass of fuel burned because, as the rocket's mass decreases, the same force causes greater acceleration. The rocket's acceleration increases as the mass decreases, leading to a change of velocity that depends on the cumulative effect of the mass loss and force application over time.