Question

A particle is moving eastwards with a velocity of $5m/s$. In $10s$, the velocity changes to $5m/s$ northwards. The average acceleration in this time is.

• A. Zero
• B. $\frac{1}{\sqrt{2}}m/s^2$ towards north-west
• C. $\frac{1}{\sqrt{2}}m/s^2$ towards north-east
• D. $\frac{1}{2}m/s^2$ towards north west

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}m/s^2$ towards north-west

The initial velocity of the particle, v=$5\hat{i}$

After some time velocity changes to $5\hat{j}$

Change in velocity dv= $5\hat{j}-5\hat{i}$

Time taken t= 10 sec.

Average acceleration =$|\frac{dv}{t}|=|\frac{1}{2}(\hat{j}-\hat{i})|=\frac{1}{\sqrt{2}}m/s^2$

The direction is north-west making 135 degrees with east as evident from its components.