A cylindrical roller has a radius of 54.7 cm and rotates according to
\[
\theta(t)=\left(1.28 \frac{\mathrm{rad}}{\mathrm{~s}}\right) t+\left(2.31 \frac{\mathrm{rad}}{\mathrm{~s}^{2}}\right) t^{2}-\left(0.520 \frac{\mathrm{rad}}{\mathrm{~s}^{3}}\right) t^{3}
\]
a. Find the angular position, angular velocity, and angular acceleration of the roller at a time of 2.00 s .
b. Find the average angular velocity and the average angular acceleration for the first 2.00 s .
c. Find the maximum angular velocity of the roller.
d. Find the maximum tangential speed of a point on the edge of the roller.
