Question

The displacement-time graphs of two particles $A$ and $B$ are straight lines making angles of $30^{\circ}$ and $60^{\circ}$ respectively with the time axis. If the velocity of $A$ is $v_A$ and that of $B$ is $v_B$, the value of $v_A / v_B$ is

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

Answer 1

Answer: (D)

$v _{ A }=\tan 30^{\circ}$ and $v _{ B }=\tan 60^{\circ}$
$\therefore \frac{ v _{ A }}{ v _{ B }}=\frac{\tan 30^{\circ}}{\tan 60^{\circ}}=\frac{1 / \sqrt{3}}{\sqrt{3}}=\frac{1}{3}$