Physics - Work Power & Energy Question with Solution | TestHub

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