Solve 1-D dynamics problem using integration and ??? 1. The problem statement, all variables and given/known data A 75kg rocket is launched directly upward. The force on the rocket due to its engine decreases from 5000N to 0N as a quadratic function of time. The rocket reaches a speed of 200m/s during the time interval that its engine fires. 2. Relevant equations Ft = 5000 - At2 a = -1/75At2 + 66.6 (the force of thrust minus force of gravity divided by mass) 3. The attempt at a solution I tried integrating acceleration and end up with both a time and a variable A left that I can't seem to get rid of. With no given time or position beyond the start, I'm at a loss as to how to solve this? I even tried impulse-momentum and comparing it to the integrated acceleration (velocity), but I ended up getting a negative time for my answer. Also, this question is in a part of our textbook that is only analyzing kinematics and dynamics, so it seems as if they aren't even expecting you to use conservation laws on it. If anyone can help point me in the right direction, I'd appreciate it.