The displacement-time graphs of two particles A and $\mathrm{B}$ are straight lines making angles of…

The displacement-time graphs of two particles A and $\mathrm{B}$ are straight lines making angles of $30^{\circ}$ and $60^{\circ}$ respectively with the time axis. If the velocity of A is $\mathrm{v}_{\mathrm{A}}$ and that of $\mathrm{B}$ is $\mathrm{v}_{\mathrm{B}}$, the value of $\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}}$ is
  1. $1 / 2$
  2. $1 / \sqrt{3}$
  3. $\sqrt{3}$
  4. $1 / 3$

Solution

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

Asked in: JEE Mains - Motion In One Dimension - Test 3

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