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Starting from rest at t = 0 s, a wheel undergoes a constant angular acceleration. When t = 1.6 s, the angular velocity of the wheel is 5.9 rad/s. The acceleration continues until t = 19 s, when the acceleration abruptly changes to 0 rad/s2. Through what angle does the wheel rotate in the interval t = 0 s to t = 47 s?

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  1. v = Vi + a t

    theta = theta zero + Vi t + (1/2) a t^2

    when t = 0, v = 0
    v = a t
    5.9 = a(1.6)
    so a = 3.69 radians/s^2

    now at 19 seconds:
    v = 0 + 3.69 (19) = 70.1 radians/s
    theta = 0 + 0 t + (.5)(3.69)(19)^2
    = 666 radians

    NOW continues at 70.1 rad/s for
    47 - 19 = 28 seconds
    so goes 28*70.1 = 1963 radians more

    1963 + 666 = 2629 radians

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