A body of mass 1, kg begins to move under the | vedclass

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(C) Given: Force $\overrightarrow{F} = (2t\hat{i} + 3t^2\hat{j})\, N$ and mass $m = 1\, kg$.Acceleration of the body is given by $\overrightarrow{a} =

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$(2t^3 + 3t^5)\, W$

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(C) Given: Force $\overrightarrow{F} = (2t\hat{i} + 3t^2\hat{j})\, N$ and mass $m = 1\, kg$.Acceleration of the body is given by $\overrightarrow{a} = \frac{\overrightarrow{F}}{m} = \frac{2t\hat{i} + 3t^2\hat{j}}{1} = (2t\hat{i} + 3t^2\hat{j})\, m/s^2$.Velocity $\overrightarrow{v}$ at time $t$ is obtained by integrating acceleration with respect to time: $\overrightarrow{v} = \int \overrightarrow{a} dt = \int (2t\hat{i} + 3t^2\hat{j}) dt = t^2\hat{i} + t^3\hat{j}\, m/s$.Power $P$ developed by the force is the dot product of force and velocity: $P = \overrightarrow{F} \cdot \overrightarrow{v}$.$P = (2t\hat{i} + 3t^2\hat{j}) \cdot (t^2\hat{i} + t^3\hat{j}) = (2t)(t^2) + (3t^2)(t^3) = 2t^3 + 3t^5\, W$.

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

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