Previous Year NEET Question- Optics L-9

Question: A particle has initial velocity $(2 \vec{i}+3 \vec{j})$ and acceleration $(0.3 \vec{i}+0.2 \vec{j})$. The magnitude of velocity after 10 seconds will be#

A) $9 \sqrt{2}$

B) $5 \sqrt{2}$

C) 5 units

D) 9 units

Answer: $5 \sqrt{2}$#

Sol:#

$$ \vec{P}=\text { vector sum }=\vec{A}+\vec{B} $$ $$ \vec{Q}=\text { Vector difference }=\vec{A}-\vec{B} $$

Since $\vec{P}$ and $\vec{Q}$ are perpendicular $$ \begin{alignedat} & \therefore \vec{P} \cdot \vec{Q}=0 \Rightarrow(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0 \ & \Rightarrow A^2=B^2=|\vec{A}|^2=|\vec{B}|^2 \end{aligned} $$