Question

A particle has initial velocity $ ( 2 \vec{i} + 3 \vec{j})$ and acceleartion ($ 0 . 3 \vec{i} + 0 . 2 \vec{j})$ The magnitude of velocity after $10$ seconds will be

• A. 9 $ \sqrt 2 $ units
• B. 5 $ \sqrt 2 $ units
• C. 5 units
• D. 9 units

Answer 1

Answer: (B)

Here, $\vec{u}=2 \hat{i}+3 \hat{j}, \vec{a}=0.3 \hat{i}+0.2 \hat{j}, t=10 s$
As $\vec{v}=\vec{u}+\vec{a} t$
$\therefore \vec{v}=(2 \hat{i}+3 \hat{j})+(0.3 \hat{i}+0.2 \hat{j})(10)$
$=2 \hat{i}+3 \hat{j}+3 \hat{i}+2 \hat{j}=5 \hat{i}+5 \hat{j}$
$|\vec{v}|=\sqrt{(5)^{2}+(5)^{2}}=5 \sqrt{2}$ units