## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$\alpha = 0.75~rad/s^2$
We can find the average angular speed during the period of acceleration; $\omega_{ave} = \frac{3.5~rev/s+6.0~rev/s}{2} = 4.75~rev/s$ We can find the average speed of the car during the acceleration period; $v_{ave} = \omega_{ave}~(2\pi~r)$ $v_{ave} = (4.75~rev/s)[(2\pi)(0.32)~m/rev]$ $v_{ave} = 9.55~m/s$ We can find the time to travel 200 meters; $t = \frac{x}{v_{ave}} = \frac{200~m}{9.55~m/s}$ $t = 20.9 ~s$ We can find the angular acceleration; $\alpha = \frac{\omega_f-\omega_0}{t}$ $\alpha = \frac{(6.0~rev/s-3.5~rev/s)(2\pi ~rad/rev)}{20.9~s}$ $\alpha = 0.75~rad/s^2$