Question

A particle moves with a velocity, $\overrightarrow{v}=(5\hat{i}-3\hat{j}+6\hat{k})\text{m/s}$ at an instant, under the influence of a constant force, $\overrightarrow{F}=(10\hat{i}+10\hat{j}+20\hat{k})\text{N}$. The instantaneous power applied to the particle is

• A. $110\text{W}$
• B. $120\text{W}$
• C. $140\text{W}$
• D. $150\text{W}$

Answer 1

The correct option is C $140\text{W}$

We know that, instantaneous power,

$P=\overrightarrow{F}\cdot \overrightarrow{v}$

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

$\Rightarrow P=(10\times 5)+(10\times -3)+(20\times 6)$

$\Rightarrow P=140\text{W}$

Hence, option $\left(C\right)$ is the correct answer.