An object of mass 1000 g experiences a time dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N\). The power generated by the force at time \(t\) is :

\(\begin{aligned} & \overrightarrow{\mathrm{F}}=(2 t \hat{\mathrm{i}}+3 \mathrm{t} \hat{\mathrm{j}}) \mathrm{N} \\ & \mathrm{m}=1000 \mathrm{gm}=1 \mathrm{~kg} \\ & \overrightarrow{\mathrm{~F}}=m \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{a}}=2 \mathrm{t} \hat{\mathrm{i}}+3 \mathrm{t}^2 \hat{j} \\ & \frac{\mathrm{~d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}=2 t \hat{\mathrm{i}}+3 \mathrm{t}^2 \hat{\mathrm{j}}\end{aligned}\)
\(\vec{v}=t^2 \hat{i}+t^3 \hat{j}\)
Power, \(\mathrm{P}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{v}}\)
\(\begin{aligned} & P=\left(2 t \hat{i}+3 t^2 \hat{j}\right) \cdot\left(t^2 \hat{i}+t^3 \hat{j}\right) \\ & P=\left(2 t^3+3 t^5\right) W\end{aligned}\)