Answer
$\omega=42.7 rad/s$
$\theta=42.7 rad$
Work Step by Step
We can determine the required angular velocity and the angular displacement as follows:
We know that
$d\omega=\alpha dt$
$\implies \int_0^{\omega}=\int_0^t 2t^2 dt$
This simplifies to:
$\omega=\frac{2}{3}t^3$
At $t=4s$
$\omega=\frac{2}{3}(4)^3$
$\implies \omega=42.7 rad/s$
Now $d\theta=\omega dt$
$\implies \int_0^{\theta}=\int_0^t \frac{2}{3} t^3 dt$
This simplifies to:
$\theta=\frac{1}{6}t^4$
At $t=4s$
$\implies \theta=\frac{1}{6}(4)^4$
$\implies \theta=42.7 rad$
