The motor M begins rotating at an angular rate = a(1 e bt ). If

The motor M begins rotating at an angular rate ω = a(1 − e^bt). If the pulleys and fan have the radii shown, determine the magnitudes of the velocity and acceleration of point P on the fan blade when t = t₁. Also, what is the maximum speed of this point?

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Given: a = 4 rad b = -1 S - S = 0.5 s r1 = 1 in r2 = 4 in r3 = 16 in