Final answer:
The force required to keep a rocket ship at a constant velocity in deep space is zero due to Newton's first law of motion. However, during acceleration phases, a constant applied force results in increased acceleration as fuel mass decreases.
Step-by-step explanation:
The force required to keep a rocket ship moving at a constant velocity in deep space is equal to zero. This is because, once in deep space, and assuming no other external forces like gravity from nearby planets or stars are acting on it, a rocket will continue to move at a constant velocity due to Newton's first law of motion, which states that an object in motion will stay in motion at the same velocity unless acted upon by an external force. Additionally, if the rocket is not burning fuel and there's no air resistance, as is the case in the vacuum of space, no additional force is needed to maintain constant velocity.
However, during the process of acceleration, if the rocket is burning fuel, the situation is different as explained by the strategy given in the context. The applied force is constant since the fuel is being ejected at a consistent rate, but because the rocket's mass decreases as fuel is spent, the acceleration of the rocket increases over time. Therefore, during acceleration, the force required to increase speed is directly proportional to the mass of the rocket which changes as fuel is burned and this relationship is not linear.