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A 3000-kg spaceship is moving away from a space station at a constant speed of 3 m/s. The astronaut in the spaceship decides to return to the space station by switching on engines that expel fuel so that the sum of the forces exerted on the spaceship by the expelled fuel points toward the space station. What is the magnitude of the minimum force needed to bring the spaceship back to the space station

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Answer:

P = m (v2 - v1)     change in momentum

P = - m v1  if v2 is to be zero

F = P / t     change in momentum equals applied force

F = m a = - m v1 / t

a = -v1 / t     or a * t = -v1`

Any combination of a and t that is greater than v1 will bring the space station to a halt

If a is small then t must be large

Any applied force will eventually bring the ship to a halt and then begin the acceleration towards the starting point

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