To determine the rocket's acceleration, the discussion revolves around two phases: the first phase with a burn time of 30 seconds and the second phase of free fall lasting 270 seconds. Participants clarify that the rocket's motion is vertical, with gravity affecting its acceleration during the second phase. The initial velocity at the end of the first phase is crucial for calculating the maximum altitude and the overall flight time. The final calculations suggest that the acceleration required for the rocket to achieve the desired flight characteristics is approximately 176 m/s², although some participants express confusion over the calculations and the effects of gravity. The conversation emphasizes the importance of correctly applying kinematic equations to solve for the rocket's parameters.