Velocity is maximum at mean position i.e. $x=0$
$\Rightarrow \sin \left(2 \pi t+\frac{\pi}{3}\right)=0$
$\Rightarrow\left(2 \pi t+\frac{\pi}{3}\right)=0, \pi, 2 \pi, 3 \pi \dots$
if we take $\left(2 \pi t+\frac{\pi}{3}\right)=0,$ time will come negative which is not possible. So we take $\left(2 \pi t+\frac{\pi}{3}\right)=\pi$
$\Rightarrow t=\frac{1}{3} s=0.33 s$
for other solutions, we will get higher values of time. but since it is asking for the first time after $t=0,$ the required solution will be $t=0.33 s$
$(A)\;y= sin\omega t-cos\omega t$
$(B)\;y=sin^3\omega t$
$(C)\;y=5cos\left( {\frac{{3\pi }}{4} - 3\omega t} \right)$
$(D)\;y=1+\omega t+{\omega ^2}{t^2}$
