The rotational motion of a particle is defined by the angular velocity as a function of time: w(t)=3πt(rad/s^2) + 6πt^2 (rad/s^3). Determine (a) the position and acceleration of the particle at the start of motion, (b) time to complete 3 and 1/8 cycles, and (c) the average angular velocity and acceleration from 2 seconds to 4 seconds.

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The rotational motion of a particle is defined by the angular velocity as a function of time: w(t)=3πt(rad/s^2) + 6πt^2 (rad/s^3). Determine (a) the position and acceleration of the particle at the start of motion, (b) time to complete 3 and 1/8 cycles, and (c) the average angular velocity and acceleration from 2 seconds to 4 seconds.
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