Question

A particle is moving in x-y-plane at 2 m/s along x-axis. 2 seconds later, its velocity is 4 m/s in a direction making ${60}^0$ with positive x-axis. Its average acceleration for this period of motion is :

• A. $\sqrt{5}m/s^2$, along y-axis
• B. $\sqrt{3}m/s^2$, along y-axis
• C. $\sqrt{5}m/s^2$, along at ${60}^0$ with positive x-axis
• D. $\sqrt{3}{s}^2$, along at ${60}^0$ with positive x-axis

Answer 1

The correct option is B $\sqrt{3}m/s^2$, along y-axis

Initial velocity $2\hat{i}m/s$

Time $=2sec$

Hence the new velocity will be along x-axis and y-axis (two components)

So according will also have two components

According to along y-axis

Initial velocity $=0\hat{i}m/s$

Final velocity$=4\sin 60°m/s=4\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{2}=\frac{4\sqrt{3}}{2}÷2=\sqrt{3}m/s$

Hence Option $B$ is correct.