question_answer

The displacement-time graphs of two moving Particles make angles of  and  with the X- axis. The ratio of their velocities is

A) \[1:\sqrt{3}\]                 

B) \[1:2\]

C) \[1:1\]                           

D) \[\sqrt{3}:2\]

Correct Answer: A

Solution :

Slope of the tangent to the x-t (displacement-time) graph gives velocity. In class x-t graph is a 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.

\[{{v}_{A}}=\tan 30{}^\circ =\frac{1}{\sqrt{3}}\]

\[{{v}_{B}}=\tan 45{}^\circ =1\]

\[{{v}_{B}}:{{v}_{A}}=\frac{1}{\sqrt{3}}:1=1:\sqrt{3}\]