A particle moves with a velocity horizontally under the action of a constant force The instantaneous power supplied to the particle is [2023]

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Solution

Q.
A particle moves with a velocity $(5 \hat{i} - 3 \hat{j} + 6 \hat{k})$ ${ms}^{- 1}$ horizontally under the action of a constant force $(10 \hat{i} + 10 \hat{j} + 20 \hat{k})$ $N .$ The instantaneous power supplied to the particle is [2023]

1 200 W

2 Zero

3 100 W

4 140 W

Ans.
(4)

Power is scalar product of torque times velocity.

$P = \vec{F} \cdot \vec{v}; P = (10 \hat{i} + 10 \hat{j} + 20 \hat{k}) \cdot (5 \hat{i} - 3 \hat{j} + 6 \hat{k})$

$P = 50 - 30 + 120,$ $P = 140$ $W$

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