Question

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the $x$-axis as shown in the figure. The ratio of their respective velocity is :

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

Answer 1

Answer: (A)

Velocity is slope of $x-t$ graph
$V =\frac{ dx }{ dt }=\tan \theta $
$\frac{ V _{1}}{ V _{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}=\frac{1}{\sqrt{3}}$