Question

A particle moves towards east with a speed $5m/s$. After $10$ seconds its direction changes towards north with the speed being the same. The average acceleration of the particle is

• A. zero
• B. $\frac{1}{\sqrt{2}}m{s}^{2}N-W$
• C. $\frac{1}{\sqrt{2}}m{s}^{2}N-E$
• D. $\frac{1}{\sqrt{2}}m{s}^{2}S-W$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}m{s}^{2}N-W$

Let $\hat{i}\&\hat{j}$ be unit vector along east and north direction respectively
change in velocity $\overrightarrow{\Delta v}=5\hat{j}-5\hat{i}$, it is along NW direction and
$\left|\overrightarrow{\Delta v}\right|=\sqrt{5^2+5^2}=5\sqrt{2}$
and average acceleration $=\frac{5\sqrt{2}}{10}=\frac{1}{\sqrt{2}}m{s}^{-2}$