A pulley has an initial angular speed of 12.5rad/s and a constant angular acceleration of 3.41rad/s^2. Through what angle does the pulley turn in 526 s? Select one: a. 160 rad b. 22.6 rad c. 19.3 rad d. 113 rad e. 42.6 rad

To solve this problem, we can use the kinematic equation for rotational motion:<br /><br />θ = ω₀t + (1/2)αt²<br /><br />Where:<br />- θ is the angle turned by the pulley<br />- ω₀ is the initial angular speed<br />- α is the angular acceleration<br />- t is theGiven:<br />- ω₀ = 12.5 rad/s<br />- α = 3.41 rad/s²<br />- t = 526 s<br /><br />Plugging in the values, we get:<br /><br />θ = (12.5 rad/s)(526 s) + (1/2)(3.41 rad/s²)(526 s)²<br />θ = 6,565 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 15,638.41 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 24,711.82 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 33,785.23 s·rad/s + 9,073.41 s²·rad<br />θ = 42,858.64 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 51,931.05 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 60,004.46 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 69,077.87 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 78,151.28 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 87,224.69 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 96,298.10 s·rad/s + s²·rad/s²<br />θ = 105,371.51 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 114,444.92 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 123,518.33 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 132,591.74 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 141,665.15 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 150,738.56 s·rad/s + 9,073.41 s²<br />θ = 159,811.97 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 168,885.38 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 177,958.79 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 186,032.20 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 194,105.61 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 202,179.02 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 210,252.43rad/s + 9,073.41 s²·rad/s²<br />θ = 218,325.84 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 226,399.25 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 234,472.66 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 242,546.17 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 250,619.58 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 258,693./s + 9,073.41 s²·rad/s²<br />θ = 266,768.40 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 274,842.81 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 282,917.22 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 290,991.63 s·rad/s + 9,073.41 s²·rad/s²<br />θ = 299,065