Answer
$\alpha = 0.75~rad/s^2$
Work Step by Step
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;
$\alpha = \frac{\omega_f-\omega_0}{t}$
$\alpha = \frac{(6.0~rev/s-3.5~rev/s)(2\pi ~rad/rev)}{20.9~s}$
$\alpha = 0.75~rad/s^2$
