Question

lf a body starts with a velocity $2\hat{i}-3\hat{j}+11\hat{k}m{s}^{-1}$ and moves with an acceleration of $10\hat{i}+10\hat{j}+10\hat{k}m{s}^{-2}$ then its velocity after $0.25$ s will be:

• A. $\frac{1}{2}\sqrt{811}m{s}^{-1}$
• B. $\sqrt{\frac{811}{2}}m{s}^{-1}$
• C. $\sqrt{811}m{s}^{-1}$
• D. $2\sqrt{811}m{s}^{-1}$

Answer 1

The correct option is A $\frac{1}{2}\sqrt{811}m{s}^{-1}$

Given that: $\overrightarrow{u}=2\hat{i}-3\hat{j}+11\hat{k}m/s$

$\overrightarrow{a}=10\hat{i}+10\hat{j}+10\hat{k}m/s^2$

$t=0.25s$

By using: $v=u+at$

$\overrightarrow{v}=2\hat{i}-3\hat{j}+11\hat{k}+(10\hat{i}+10\hat{j}+10\hat{k})0.25$

$\overrightarrow{v}=2\hat{i}-3\hat{j}+11\hat{k}+(2.5\hat{i}+2.5\hat{j}+2.5\hat{k})$ $\overrightarrow{v}=4.5\hat{i}-0.5\hat{j}+13.5\hat{k}$

Therefore magnitude of velocity $\overrightarrow{v}$

$v=\sqrt{{4.5}^2+{0.5}^2+{13.5}^2}$

$v=\sqrt{20.25+0.25+182.25}$

$v=\sqrt{202.75}$

$v=\frac{1}{2}\sqrt{811}m/s$