A roller in a printing press turns through an angle θ(t) given by θ(t) = γt^{2} - βt^{3} , where γ = 3.20 rad/s^{2} and β = 0.500 rad/s^{3}.

a) Calculate the angular velocity of the roller as a function of time.

b) Calculate the angular acceleration of the roller as a function of time.

c) What is the maximum positive angular velocity?

d) At what value of t does it occur?

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