Question

A body of mass $2\text{kg}$ is moving uniformly with the velocity of $(2\hat{i}+3\hat{j}+4\hat{k})\text{m/s}$. Find its kinetic energy.

• A. $21\text{J}$
• B. $25\text{J}$
• C. $37\text{J}$
• D. $29\text{J}$

Answer 1

The correct option is D $29\text{J}$

Given mass$\left(m\right)$=$2\text{kg}$ and velocity,
$\overrightarrow{v}$ $=2\hat{i}+3\hat{j}+4\hat{k}\text{m/s}$

We know that,
Kinetic energy $=\frac{1}{2}m\overrightarrow{v}.\overrightarrow{v}=\frac{1}{2}m(\overrightarrow{|v|}{)}^2$
The magnitude of velocity will be,

$|\overrightarrow{v}|=\sqrt{2^2+3^3+4^2}=\sqrt{29}\text{m/s}$

Hence, kinetic energy will be,

$=\frac{1}{2}\times 2\times (\sqrt{29}{)}^2$

$=29\text{J}$

Hence option D is the correct answer