Question

A particle is moving with a velocity of $5m{s}^{-1}$ towards east and its velocity changes to $5m{s}^{-1}$ north in 10 s. Then the acceleration of the particle is:

• A. $\sqrt{2}NW$
• B. $\frac{1}{\sqrt{2}}NE$
• C. $\frac{1}{\sqrt{2}}NW$
• D. $\sqrt{2}NE$

Answer 1

The correct option is A $\sqrt{2}NW$

Denoting east by $\hat{i}$ and North by $\hat{j}$ and west by $-\hat{i}$

we get ${\overrightarrow{V}}_1=5\hat{i}$

and ${\overrightarrow{V}}_2=5\hat{j}$

change in velocity is $\Delta \overrightarrow{V}={\overrightarrow{V}}_2-{\overrightarrow{V}}_1=5\hat{j}-5\hat{i}$

so acceleration will be $\frac{\Delta \overrightarrow{V}}{time}=0.5\hat{j}-0.5\hat{i}$

magnitude is $0.5\sqrt{2}=\frac{\sqrt{2}}{2}=\sqrt{2}$ direction is $bisector$ of angle between north and west so $NW$