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

Answer 1

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