Q.
The displacement-time graphs of two moving particles make angles of $30{^\circ}\ and\ 45{^\circ}$ with the $x -$axis. The ratio of their velocities is
A) $1\ :\ \sqrt{3}$
B) $1\ :2$
C) $1\ :1$
D) $\sqrt{3}\ :2$
Explanation
(a) Slope of displacement time-graph is velocity
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{v_{1}}{v_{2}} = \frac{\tan\theta_{1}}{\tan\theta_{2}} = \frac{\tan{30{^\circ}}}{\tan{45{^\circ}}} = \frac{1}{\sqrt{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{1}\ :v_{2} = 1\ :\ \sqrt{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.