An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2 t \hat{i}+3 t^{2} \hat{

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

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(c) : $\vec{F}=\left(2 t \hat{i}+3 t^{2} \hat{j}ight) \mathrm{N}$ $$ \begin{aligned} m & =1000 \mathrm{gm}=1 \mathrm{~kg} \ \vec{F} & =m \ddot{a} \Rightarrow \vec{a}=2 t \hat{i}+3 t^{2} \hat{j} \end{aligned} $$ $	herefore \quad \frac{d \vec{v}}{d t}=2 t \hat{i}+3 t^{2} \hat{j}$\ or $\vec{v}=t^{2} \hat{i}+t^{3} \hat{j}$\ Power, $P=\vec{F} \cdot \vec{v}$ $$ \begin{aligned} & P=\left(2 t \hat{i}+3 t^{2} \hat{j}ight) \cdot\left(t^{2} \hat{i}+t^{3} \hat{j}ight) \ & P=\left(2 t^{3}+3 t^{5}ight) \mathrm{W} \end{aligned} $$