The displacement-time graphs of two moving particles make angles … - Vidyadip

MCQ

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

✓
$1:\sqrt{3}$
B
$1:2$
C
$1:1$
D
$\sqrt{3}:2$

✓

Answer

Correct option: A.

$1:\sqrt{3}$

In case $x-t$ graph the graphs are a straight line, slope of the straight line gives velocity of the particle.
Slope $=\tan \theta,$
where $\theta$ is the angle which the tangent to the curve makes with the horizontal in anti$-$clockwise direction.
$\text{v}_\text{A}=\tan30^\circ=\frac{1}{\sqrt{3}},$
$\text{v}_\text{B}=\tan45^\circ=1$
$\Rightarrow\text{v}_\text{A}:\text{v}_\text{B}=\frac{1}{\sqrt{3}}:1$
$=1:\sqrt{3}$

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