A particle moves with a velocity vec{v} = 5ha | vedclass

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(C) The instantaneous power $P$ delivered by a force $\vec{F}$ to a particle moving with velocity $\vec{v}$ is given by the dot product of the force a

Vedclass · Accepted Answer

$140$

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(C) The instantaneous power $P$ delivered by a force $\vec{F}$ to a particle moving with velocity $\vec{v}$ is given by the dot product of the force and velocity vectors:$P = \vec{F} \cdot \vec{v}$Given:$\vec{v} = (5\hat{i} - 3\hat{j} + 6\hat{k}) 	ext{ m/s}$$\vec{F} = (10\hat{i} + 10\hat{j} + 20\hat{k}) 	ext{ N}$Substituting these values into the formula:$P = (10\hat{i} + 10\hat{j} + 20\hat{k}) \cdot (5\hat{i} - 3\hat{j} + 6\hat{k})$Using the dot product rule $(a_x\hat{i} + a_y\hat{j} + a_z\hat{k}) \cdot (b_x\hat{i} + b_y\hat{j} + b_z\hat{k}) = a_x b_x + a_y b_y + a_z b_z$:$P = (10 	imes 5) + (10 	imes -3) + (20 	imes 6)$$P = 50 - 30 + 120$$P = 140 	ext{ W}$ (or $	ext{J/s}$)Thus,the instantaneous power is $140 	ext{ J/s}$.

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

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