Question

From the position time graph for two particles and B is shown below. Graph A and particles A making angles ${60}^{\circ }$ and ${30}^{\circ }$ with the time axis. The ratio of velocities $v_A:v_B$ is

• A. $1:1$
• B. $4:1$
• C. $\sqrt{2}:1$
• D. $1:3$

Answer 1

Answer: (D)

$1:3$

The slope of the distance - time graph gives the speed of the object.

For the particle $A$, the slope of the line is $tan{\theta }_1=tan30=\frac{1}{\sqrt{3}}$

For the particle $B$, the slope of the line is $tan{\theta }_2=tan60=\sqrt{3}$

Thus, ratio of the velocities, $\frac{v_A}{v_B}=\frac{tan30}{tan60}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}$

So, the ratio is $1:3$