Starting from rest, the disc completes [tex]\theta[/tex] revolutions after [tex]t[/tex] seconds according to
[tex]\theta=\dfrac\alpha2t^2[/tex]
with angular acceleration [tex]\alpha[/tex]. It completes 10 rev in 2 s, which means
[tex]10\,\mathrm{rev}=\dfrac\alpha2(2\,\mathrm s)^2\implies\alpha=5\dfrac{\rm rev}{\mathrm s^2}[/tex]
Find the time it takes to complete 20 rev with this acceleration:
[tex]20\,\mathrm{rev}=\dfrac12\left(5\dfrac{\rm rev}{\mathrm s^2}\right)t^2\implies t=\sqrt8\,\mathrm s\approx2.83\,\mathrm s[/tex]
so it takes approximately 0.83 s to complete 10 more rev.
