This problem is based on a rocket that has launched from rest and is moving fast

Question

This problem is based on a rocket that has launched from rest and is moving faster and faster upwards originally at rest until its fuel runs out and it coasts to a stop at maximum height. Up is positive. Ignore air resistance. Recall how the sum force and acceleration are related. Assume that the mass of the rocket does not change. Which of the following acceleration versus time plots accurately depicts the acceleration from rest to peak height of flight.  (please explain also)

Explanation / Answer

final velocity turns out to be zero when at max. height

so area9 under acceleration - time graph should be zero should best represent

so only (c) can turn out to be zero

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