Answer:
After 8.5 s
Explanation:
We can use the equivalent suvat equation for rotational motions to find the angular acceleration of the wheel:
[tex]\theta = \omega_i t + \frac{1}{2}\alpha t^2[/tex]
where:
[tex]\theta = 2\pi rad[/tex] is the angular displacement covered during the first 6.0 s (the angle corresponding to one revolution)
[tex]\omega_i=0[/tex]is the initial angular velocity
[tex]\alpha[/tex] is the angular acceleration
t = 6.0 s is the time
Solving for  [tex]\alpha[/tex],
[tex]\alpha = \frac{2\theta}{t^2}=\frac{2(2\pi)}{6.0)^2}=0.349 rad/s^2[/tex]
Now we want to find instead the time t after which the wheel has completed two revolutions, so the time t at which
[tex]\theta = 4 \pi[/tex]
Using again the same equation as before and solving for t, we find:
[tex]t=\sqrt{\frac{2\theta}{\alpha}}=\sqrt{\frac{2(4\pi)}{0.349}}=8.5 s[/tex]
