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, $\vec{u}=2\hat{i}+3\hat{j},\vec{a}=0.3\hat{i}+0.2\hat{j},t=10s$
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