The displacement-time graph for two particles | vedclass

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(D) The velocity of a particle in a displacement-time graph is given by the slope of the line,which is $	an 	heta$,where $	heta$ is the angle the l

Vedclass · Accepted Answer

$1: 3$

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(D) The velocity of a particle in a displacement-time graph is given by the slope of the line,which is $	an 	heta$,where $	heta$ is the angle the line makes with the time axis ($X$-axis).From the given graph:For particle $A$,the angle with the $X$-axis is $	heta_A = 45^{\circ} - 15^{\circ} = 30^{\circ}$.Thus,the velocity of $A$ is $v_A = 	an 30^{\circ} = \frac{1}{\sqrt{3}}$.For particle $B$,the angle with the $X$-axis is $	heta_B = 45^{\circ} + 15^{\circ} = 60^{\circ}$.Thus,the velocity of $B$ is $v_B = 	an 60^{\circ} = \sqrt{3}$.The ratio $\frac{v_A}{v_B}$ is calculated as:$\frac{v_A}{v_B} = \frac{	an 30^{\circ}}{	an 60^{\circ}} = \frac{1/\sqrt{3}}{\sqrt{3}} = \frac{1}{3}$.Therefore,the ratio $v_A : v_B$ is $1: 3$.

The displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

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