Answer
At $t=14s$, the angular velocity of the object is $32rad/s$
Work Step by Step
We have $\omega_0=0rad/s$. After $t=7s$, $\omega=16rad/s$
The angular acceleration of the object is $$\alpha=\frac{\omega-\omega_0}{t}=\frac{16}{7}rad/s^2$$
Next, we still set $\omega_0=0rad/s$. After $t=14s$, the angular velocity of the object is $$\omega=\omega_0+\alpha t=\frac{16}{7}\times14=32rad/s$$
