Q103 / 200 · NEET 2012 (Screening) · Physics
A particle has initial velocity $(2 \mathbf{i}+3 \mathbf{j})$ and acceleration $(0.3 \mathbf{i}+0.2 \mathbf{j})$. The magnitude of velocity after $10 \mathrm{~s}$ will be
- A$9 \sqrt{2}$ units
- Correct answerB$5 \sqrt{2}$ units
- C5 units
- D9 units
Solution
\(\begin{aligned}
& \text {Here, } \vec{u}=2 \hat{i}+3 \hat{j} \text {, } \\
& \vec{a}=0.3 \hat{i}+0.2 \hat{j}, t=10 \mathrm{~s} \\
& \text { As } \bar{v}=\bar{u}+\vec{a} t \\
& \bar{v}=(2 \hat{i}+3 \hat{j})+(0.3 \hat{i}+0.2 \hat{j})(10) \\
& =2 \hat{i}+3 \hat{j}+3 \hat{i}+2 \hat{j}=5 \hat{i}+5 \hat{j} \\
& |\vec{v}|=\sqrt{(5)^2+(5)^2} \\
& =5 \sqrt{2} \text { units }
\end{aligned}\)
Hence, the correct answer is option: 'B'.