A body of mass 2 text{ kg} begins to move und | vedclass

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(B) Given mass $m = 2 	ext{ kg}$ and force $\vec{F} = (2t\hat{i} + 6t^2\hat{j}) 	ext{ N}$.Acceleration $\vec{a} = \frac{\vec{F}}{m} = \frac{2t\hat{i

Vedclass · Accepted Answer

$200$

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(B) Given mass $m = 2 	ext{ kg}$ and force $\vec{F} = (2t\hat{i} + 6t^2\hat{j}) 	ext{ N}$.Acceleration $\vec{a} = \frac{\vec{F}}{m} = \frac{2t\hat{i} + 6t^2\hat{j}}{2} = (t\hat{i} + 3t^2\hat{j}) 	ext{ m/s}^2$.Velocity $\vec{v} = \int \vec{a} \, dt = \int (t\hat{i} + 3t^2\hat{j}) \, dt = (\frac{t^2}{2}\hat{i} + t^3\hat{j}) 	ext{ m/s}$ (assuming initial velocity is zero).At $t = 2 	ext{ s}$:Force $\vec{F} = 2(2)\hat{i} + 6(2^2)\hat{j} = (4\hat{i} + 24\hat{j}) 	ext{ N}$.Velocity $\vec{v} = \frac{2^2}{2}\hat{i} + 2^3\hat{j} = (2\hat{i} + 8\hat{j}) 	ext{ m/s}$.Power $P = \vec{F} \cdot \vec{v} = (4\hat{i} + 24\hat{j}) \cdot (2\hat{i} + 8\hat{j}) = (4 	imes 2) + (24 	imes 8) = 8 + 192 = 200 	ext{ W}$.

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