A body of mass $2 \mathrm{~kg}$ begins to move under the action of a time dependent force given by $\vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N$. The power developed by the force at the time $t$ is given by:
Solution
<p>$$\begin{aligned}
& \vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N \\
& \vec{F}=m \vec{a}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) \\
& \vec{a}=\frac{\vec{F}}{m}=\left(3 t \hat{i}+3 t^2 \hat{j}\right) \\
& \vec{v}=\int_\limits0^t \vec{a} d t=\frac{3 t^2}{2} \hat{i}+t^3 \hat{j} \\
& P=\vec{F} \cdot \vec{v}=\left(9 t^3+6 t^5\right) W
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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