(a) The angular acceleration of the wheel is given by
[tex]\alpha = \frac{\omega_f - \omega_i }{t} [/tex]
where [tex]\omega_i[/tex] and [tex]\omega_f[/tex] are the initial and final angular speed of the wheel, and t the time.
In our problem, the initial angular speed is zero (the wheel starts from rest), so the angular acceleration is
[tex]\alpha = \frac{(11.2 rad/s) - 0}{3.07 s} =3.65 rad/s^2[/tex]
(b) The wheel is moving by uniformly rotational accelerated motion, so the angle it covered after a time t is given by
[tex]\theta (t) = \omega_i t + \frac{1}{2} \alpha t^2 [/tex]
where [tex]\omega_i = 0[/tex] is the initial angular speed. So, the angle covered after a time t=3.07 s is
[tex]\theta= \frac{1}{2} \alpha t^2 = \frac{1}{2}(3.65 rad/s^2)(3.07 s)^2 = 17.2 rad [/tex]
