The angular position of a rod varies as $\theta=9 t^{2}$ (rad) where $t$ is measured in second. Consider the blue bead at $20 \mathrm{~cm}$ from the rotation axis. What is its speed in $(\mathrm{m} / \mathrm{s})$ at the moment 6 s? Give an answer with 1 decimal place such as 2.8

Step 1 ：Given the angular position of the bead as \(\theta=9 t^{2}\), we differentiate this with respect to time to get the angular velocity \(\omega\).

Step 2 ：So, \(\frac{d\theta}{dt} = \omega = 18t\).

Step 3 ：At \(t = 6\) s, the angular velocity is \(\omega = 18 * 6 = 108\) rad/s.

Step 4 ：The distance of the bead from the rotation axis is given as \(20\) cm, which is \(0.2\) m when converted to meters.

Step 5 ：Substituting these values into the formula for the speed of a point in circular motion, we get \(v = r\omega = 0.2 * 108 = 21.6\) m/s.

Step 6 ：So, the speed of the bead at the moment \(6\) s is \(21.6\) m/s. Rounded to one decimal place, this is \(\boxed{21.6}\) m/s.