A fly wheel is accelerated uniformly from rest and rotates through...

Here the angular acceleration is constant, so we have,

$\theta = \omegat + \dfrac{1}{2}\alpha{t}^{2}$.

When flywheel is rotated from rest in the first second, then ${\theta}_{1} = \dfrac{1}{2}\alpha{\left(1\right)}^{2} = 5rad$

$⇒ \alpha = 10rad{s}^{- 2}$

The angle turned by flywheel in the next second is ${\theta}_{2} = \dfrac{1}{2}\alpha{\left(2\right)}^{2} = \dfrac{1}{2}\left(10\right)\left(4\right) = 20rad{s}^{- 2}$

Thus, the angle turned during next second is $\theta = 20 - 5 = 15rad$