Question

. The displacement -time graph of two particles A and B are straight lines at angles of 30 degree and 45 degree with the time axis. Then ratio of their velocities is _________________

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

The displacement-time (s-t) graph of two particles A and B are straight lines inclined at angles of 30° and 45° with the time axis.

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find ratio of their velocities.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➢ We know that, Slope of displacement-time (s-t) graph gives velocity.

$\dag\:\boxed{\bf{\red{velocity(v)=tan\Theta=\dfrac{\Delta s}{\Delta t}}}}$

Let's calculate :D

$:\implies\tt\:\dfrac{v_A}{v_B}=\dfrac{tan30\degree}{tan45\degree}$

$:\implies\tt\:\dfrac{v_A}{v_B}=\dfrac{1}{\sqrt{3}\times 1}$

$:\implies\boxed{\bf{\purple{v_A:v_B=1:\sqrt{3}}}}$