Answer
$$\theta=9.9 \times 10^{3} \mathrm{\ rev}$$
Work Step by Step
Using Eq. $10-13$ with $t=(2.2)(60)=132$ min, the number of revolutions is
$$\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$$$$=(150 \mathrm{rev} / \min )(132 \mathrm{min})+\frac{1}{2}\left(-1.14 \mathrm{rev} / \min ^{2}\right)(132 \mathrm{min})^{2}$$$$=9.9 \times 10^{3} \mathrm{\ rev}$$
