B

To find the angular velocity, we first need to determine the angular displacement function and then differentiate it with respect to time.
Step 1: The given angular displacement is \( \theta(t) = 2t^3 + 0.5 \).
Step 2: To find the angular velocity \( \omega \), we differentiate \( \theta(t) \) with respect to time \( t \):
\( \omega(t) = \frac{d\theta}{dt} = \frac{d}{dt}(2t^3 + 0.5) \).
Step 3: Calculating the derivative:
\( \omega(t) = 6t^2 \).
Step 4: We now evaluate this expression at \( t = 2 \) seconds:
\( \omega(2) = 6(2)^2 = 6 \times 4 = 24 \) radians/second.
Therefore, the angular velocity of the particle after 2 seconds is 24 radians/second.