Question

A particle has initial velocity $(2\hat{i}+3\hat{j})$ and acceleration $(0.3\hat{i}+0.2\hat{j})$. The magnitude of velocity after $10\text{s}$ will be

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

Answer 1

The correct option is D $5\sqrt{2}units$

Let the velocity after $10\text{s}$ be $v$
$v=v_x\hat{i}+v_y\hat{j}$
$v=(u_x+a_{x}t)\hat{i}+(u_x+a_{y}t)\hat{j}$
$=(2+0.3(10\left)\right)\hat{i}+(3+0.2(10\left)\right)\hat{j}$
$=5\hat{i}+5\hat{j}$
$v=\sqrt{5^2+5^2}$
$=5\sqrt{2}units$