Question

A particle moving eastwards with $5{\text{ms}}^{-1}$. In $10\text{s}$ the velocity changes to $5{\text{ms}}^{-1}$ northwards. The average acceleration in this time is

• A. $\frac{1}{\sqrt{2}}{\text{m/s}}^2$ North-East.
• B. $\frac{1}{2}{\text{m/s}}^2$ North-West.
• C. $\frac{1}{\sqrt{2}}{\text{m/s}}^2$ North-West.
• D. Zero.

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}{\text{m/s}}^2$ North-West.

Considering eastwards as positive $x-$axis and northwards as positive $y-$axis, we can write the velocities as per the question as initial velocity of the particle $\overrightarrow{v_i}=5\hat{i}$ and the final velocity of the particle $\overrightarrow{v_f}=5\hat{j}$
So, average acceleration is given as
$\overrightarrow{a_{av}}=\frac{\overrightarrow{v_f}-\overrightarrow{v_i}}{t}=\frac{5\hat{j}-5\hat{i}}{10}=\frac{1}{2}(\hat{j}-\hat{i})$
or, $|\overrightarrow{a_{av}}|=\frac{1}{\sqrt{2}}{\text{m/s}}^2$ North-West.