Question

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

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

Answer 1

Answer: (D)

$1:\sqrt{3}$

Answer 2

By the definition, the slope of displacement-time graph is velocity.
i.e., $v=\tan \theta$
$\therefore \frac{v_{1}}{v_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$\frac{v_{1}}{v_{2}}=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}$
$\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{3}}$