A model rocket is launched vertically. The solid rocket motor produces of a thrust of T(t) = 20 - 20(t-1)^2 for 3 seconds, afterwards the rocket is acted upon by gravity alone. How far will the rocket have traveled when the motor shuts off? Assume constant gravity of 9.81 m/s2 , a constant mass of 0.148 kg, and neglect air resistance.

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