Question

The displacement time graph of two moving particles make angles of ${30}^{\circ }$ and ${45}^{\circ }$ with the X- axis is shown. The ratio of their velocities is:

• A. $\frac{\sqrt{3}}{2}$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{3}}$

Velocity = Slope of x - t graph = $tan\theta$
$V_1=tan{45}^{\circ }$
$V_1=1$
$V_2=tan{30}^{\circ }=\frac{1}{\sqrt{3}}$
$\frac{V_1}{V_2}=\frac{\sqrt{3}}{1}$
$\frac{V_2}{V_1}=\frac{1}{\sqrt{3}}$