If a force F - -7- - 6- - 2-k-N and velocity v - -6 - - k- -m-s- then the nbsp-instantaneous power is

We know that instantaneous Power P = F. nbsp;v Given, nbsp; F =( 7 î 6 ĵ + 2 k̂) N v = (6 î + k̂) m/s, ∴ nbsp;instantaneous power (P) = (7 î 6 ĵ + ...

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Standard XII

Physics

Power, Force and Velocity

If a force F ...

Question

If a force \(\overrightarrow{F}\ = (7~\hat{i} - 6~\hat{j} + 2~ \hat{k})~\text{N}\) and velocity \(\overrightarrow{v} = (6 ~\hat{i} + \hat{k}) ~\text{m/s},\) then the instantaneous power is

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Solution

We know that instantaneous Power \(P = \overrightarrow{F}. \overrightarrow{v}\)

Given,
\(\overrightarrow{F}\ =( 7~\hat{i} - 6~\hat{j} + 2 ~\hat{k})~\text{N}\)
\(\overrightarrow{v} = (6 ~\hat{i} + \hat{k}) ~\text{m/s},\)

\(\therefore\) instantaneous power
\((P) = (7~\hat{i}-6~\hat{j} + 2~\hat{k}). (6~\hat{i}+\hat{k})\)
\( = 42 + 2 = 44~\text{watts}.\)

Hence option D is the correct answer

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Power, Force and Velocity

Standard XII Physics

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