A body of mass 1 text{ kg} begins to move und | vedclass

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(A) Given mass $m = 1 	ext{ kg}$ and force $\vec{F} = t\hat{i} + 3t^2\hat{j}$.Using Newton's second law, acceleration $\vec{a} = \vec{F}/m = (t\hat{i

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$100$

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(A) Given mass $m = 1 	ext{ kg}$ and force $\vec{F} = t\hat{i} + 3t^2\hat{j}$.Using Newton's second law, acceleration $\vec{a} = \vec{F}/m = (t\hat{i} + 3t^2\hat{j}) / 1 = t\hat{i} + 3t^2\hat{j} 	ext{ m/s}^2$.Velocity $\vec{v} = \int \vec{a} dt = \int (t\hat{i} + 3t^2\hat{j}) dt = (t^2/2)\hat{i} + t^3\hat{j} 	ext{ m/s}$ (assuming initial velocity is zero).At time $t = 2 	ext{ s}$:Force $\vec{F} = 2\hat{i} + 3(2)^2\hat{j} = 2\hat{i} + 12\hat{j} 	ext{ N}$.Velocity $\vec{v} = (2^2/2)\hat{i} + 2^3\hat{j} = 2\hat{i} + 8\hat{j} 	ext{ m/s}$.Power $P = \vec{F} \cdot \vec{v} = (2\hat{i} + 12\hat{j}) \cdot (2\hat{i} + 8\hat{j}) = (2 	imes 2) + (12 	imes 8) = 4 + 96 = 100 	ext{ W}$.

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

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