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

• A

  $\sqrt{3}: 2$
• B

  $1: 1$
• C

  $1: 2$
• Correct answer
  D

  $1: \sqrt{3}$

Solution

Slope of displacement-time graph gives velocity.
$\begin{aligned} \therefore \frac{v_1}{v_2} & =\frac{\tan \theta_1}{\tan \theta_2} \\ & =\frac{\tan 30^{\circ}}{\tan 45^{\circ}}=\frac{1}{\sqrt{3}}\end{aligned}$

Hence, the correct answer is option: 'D'.