Question

A particle of mass $2\text{kg}$ is moving in $xy$ plane under the action of a force. Its velocity and acceleration at a certain instant of time are given by $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$ and $\overrightarrow{a}=(5\hat{i}+4\hat{j}){\text{m/s}}^2$. Find the power delivered by the force at that instant of time.

• A. $60\text{W}$
• B. $62\text{W}$
• C. $64\text{W}$
• D. $66\text{W}$

Answer 1

The correct option is B $62\text{W}$

Given:
Mass of particle, $m=2\text{kg}$
Instantaneous velocity, $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$
Instantaneous acceleration, $\overrightarrow{a}=(5\hat{i}+4\hat{j}){\text{m/s}}^2$

We know that the instantaneous power of a force is given by,
$P=\overrightarrow{F}.\overrightarrow{v}$
$\Rightarrow P=m\overrightarrow{a}.\overrightarrow{v}$
$\Rightarrow P=2\times (5\hat{i}+4\hat{j}).(3\hat{i}+4\hat{j})$
$\Rightarrow P=30+32=62\text{W}$