A body of mass \(1\, kg\) begins to move under the action of a time dependent force  \(\overrightarrow {\;F\;} = (2t\hat i + 3{t^2}\hat j\)) \(N\) where \(\hat i\) and \(\hat j\) are unit vectors along \(x\) and \(y\) axis. What 10.Power will be developed by the force at the time \(t\)?

\(\begin{array}{l}
\,\,\,\,\,\,\,\,Here,\,\overrightarrow F  = \left( {2t\hat i + 3{t^2}\hat j} \right)N,\,m = 1\,kg\\
Acceleration\,of\,the\,body,\,\overrightarrow a  = \frac{{\overrightarrow F }}{m}\\
\,\, = \frac{{\left( {2t\hat i + 3{t^2}\hat j} \right)N}}{{1\,kg}}\\
Velocity\,of\,the\,body\,at\,time\,t,
\end{array}\) \(\begin{array}{l}
\overrightarrow v  = \int {\overrightarrow a dt = \int {\left( {2t\hat i + 3{t^2}\hat j} \right)dt = {t^2}\hat i + {t^3}\hat j\,m{s^{ - 1}}} } \\
\therefore \,10.Power\,devloped\,by\,the\,force\,at\,time\,t,\\
P = \overrightarrow F .\overrightarrow v \, = \left( {2t\hat i + 3{t^2}\hat j} \right).\left( {{t^2}\hat i + {t^3}\hat j\,} \right)\\
W = \left( {2{t^3} + 3{t^5}} \right)W
\end{array}\)