Question

A particle moving along positive $x-$axis with a speed $5{\text{ms}}^{–1}$ suddenly changes its direction along the positive $y-$axis with the same speed. The change in velocity $\Delta \overrightarrow{v}$ of the particle is -

• A. $-5(\hat{i}+\hat{j}){\text{ms}}^{-1}$
• B. $-5(\hat{i}-\hat{j}){\text{ms}}^{-1}$
• C. $-5(-\hat{i}+\hat{j}){\text{ms}}^{-1}$
• D. $5(\hat{i}+\hat{j}){\text{ms}}^{-1}$

Answer 1

The correct option is B $-5(\hat{i}-\hat{j}){\text{ms}}^{-1}$

initial velocity ${\overrightarrow{v}}_i=5\hat{i}\text{m/s}$
final velocity ${\overrightarrow{v}}_f=5\hat{j}\text{m/s}$
So, change in velocity
$\Delta \overrightarrow{v}={\overrightarrow{v}}_f-{\overrightarrow{v}}_i=5\hat{j}-5\hat{i}$
$=5(\hat{j}-\hat{i})\text{m/s}$