Final answer:
Newton's second law states that a constant force will produce increasing acceleration as a rocket's mass decreases due to fuel burn. The rocket equation accounts for the non-linear relationship between velocity change and mass loss, while Newton's third law explains the principle of rocket propulsion.
Step-by-step explanation:
When considering the motion of a rocket that burns fuel to accelerate, Newton's second law tells us that as the rocket's mass decreases, its acceleration increases, assuming the force produced by the engines remains constant. This is because acceleration is directly proportional to the force applied and inversely proportional to the mass of the object (acceleration = force/mass). As the rocket uses up its fuel, the mass of the rocket (including any remaining fuel) becomes smaller, leading to a greater acceleration even though the thrust provided by the engine stays the same.
This resulting change in velocity due to the burning of fuel is captured by the rocket equation, which is not a simple linear relationship due to the changing mass of the rocket. Additionally, Newton's third law, which states every action has an equal and opposite reaction, underpins the fundamental mechanism of rocket propulsion. The ejection of exhaust gases at high velocity produces an equal and opposite force that propels the rocket forward. As the fuel decreases causing the rocket's mass to drop, the acceleration of the rocket correspondingly increases, achieving a maximum just before the fuel is completely exhausted.