A body of mass \(2 \mathrm{~kg}\) begins to move under the action of a time dependent force given by \(\overrightarrow{\mathrm{F}}=\left(6 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}\). The Power developed by the force at the time \(t\) is given by _______.

\(\overrightarrow{\mathrm{F}}=\mathrm{ma}=\left(6 \mathrm{t}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right)\)

\(\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\left(3 \mathrm{t}+3 \mathrm{t}^2 \hat{\mathrm{j}}\right)\)

\(\overrightarrow{\mathrm{v}}=\int_0^{\mathrm{t}} \overrightarrow{\mathrm{a}} d \mathrm{~d}=\frac{3 \mathrm{t}^2}{2} \hat{\mathrm{i}}+\mathrm{t}^3 \hat{\mathrm{j}}\)

\(\mathrm{P}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{v}}=\left(9 \mathrm{t}^3+6 \mathrm{t}^5\right) \mathrm{W}\)