Q. The displacement-time graphs of two particles $A$ and $B$ are straight lines making angles of respectively $30{^\circ}$ and $60{^\circ}$ with the time axis. If the velocity of $A$ is $v_{A}$ and that of $B$ is $v_{B}$, then the value of $\ \frac{v_{A}}{v_{B}}$ is
A) $\frac{1}{2}$
B) $\frac{1}{\sqrt{3}}$
C) $\sqrt{3}$
D) $\frac{1}{3}$
Explanation
(d) $\frac{v_{A}}{v_{B}} = \frac{tan30{^\circ}}{tan60{^\circ}} = \frac{1}{\sqrt{3}} \times \frac{1}{\sqrt{3}} = \frac{1}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.