Question

A body moves with a velocity of $3m/s$ due east and then turns due north to travel with the same velocity. If the total time of travel is $6s$, the acceleration of the body is :

• A. $\sqrt{3}m/s^2$ towards north west
• B. $\frac{1}{\sqrt{2}}m/s^2$ towards north west
• C. $\sqrt{2}m/s^2$ towards north east
• D. none of the above

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}m/s^2$ towards north west

Final velocity $=3\hat{j}$ (towards y direction or North)
Initial velocity $=3\hat{i}$ ( towards x direction or East)
So, change in velocity $=3\hat{j}-3\hat{i}=3(\hat{j}-\hat{i})$ $m/s$
Total time $=$ $6s$
So, acceleration $=|3\frac{(\hat{j}-\hat{i})}{6}|=|\frac{(\hat{j}-\hat{i})}{2}|=|\frac{1}{2}(\hat{j}-\hat{i})|=\frac{1}{\sqrt{2}}$ $m/s^2$ in the direction of north west.