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The angular acceleration of a wheel, as a function of time, is α = 5.0 t^{2} - 8.5 t, where α is in rad/s^{2} and t is in seconds. If the wheel starts from rest (θ = 0, ω = 0, at t = 0), determine a formula for

a) the angular velocity ω as a function of time

b) the angular position θ as a function of time

c) evaluate ω at t = 4.0 s

d) evaluate θ at t = 4.0 s

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Based on our data, we think this problem is relevant for Professor Efthimiou's class at UCF.