The angular displacement of a body on a circular orbit is given by the function: $$ \theta(t) = 2t^2 + 5t + 5 $$ where $t$ is in seconds. To calculate the angular velocity, we need to find the derivative of the angular displacement with respect to time. Angular velocity $\omega(t)$ is defined as $\omega(t) = \frac{d\theta}{dt}$. Step 1: Differentiate the angular displacement function with respect to time. $$ \omega(t) = \frac{d}{dt}(2t^2 + 5t + 5) $$ $$ \omega(t) = \frac{d}{dt}(2t^2) + \frac{d}{dt}(5t) + \frac{d}{dt}(5) $$ $$ \omega(t) = 2(2t) + 5(1) + 0 $$ $$ \omega(t) = 4t + 5 $$ Step 2: Substitute $t = 2 \text{ s}$ into the angular velocity function. $$ \omega(2) = 4(2) + 5 $$ $$ \omega(2) = 8 + 5 $$ $$ \omega(2) = 13 \text{ rad/s} $$ The angular velocity at $t = 2 \text{ s}$ is $\boxed{13 \text{ rad/s}}$.