(C) The velocity of a particle is given by the slope of the displacement-time graph.$V = \frac{dx}{dt} = \tan \theta$Given the angles $\theta_1 = 30^{

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(C) The velocity of a particle is given by the slope of the displacement-time graph.$V = \frac{dx}{dt} = \tan \theta$Given the angles $\theta_1 = 30^{\circ}$ and $\theta_2 = 45^{\circ}$,the ratio of their velocities is:$\frac{V_1}{V_2} = \frac{\tan 30^{\circ}}{\tan 45^{\circ}}$Since $\tan 30^{\circ} = \frac{1}{\sqrt{3}}$ and $\tan 45^{\circ} = 1$,we have:$\frac{V_1}{V_2} = \frac{1/\sqrt{3}}{1} = \frac{1}{\sqrt{3}}$Thus,the ratio is $1: \sqrt{3}$.

Class 11 Physics Motion in Straight Line Instantaneous Velocity and Speed and Velocity-time Graph

Medium

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time-axis as shown in the figure. The ratio of their respective velocities is:

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

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Motion in Straight Line

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Instantaneous Velocity and Speed and Velocity-time Graph

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The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time-axis as shown in the figure. The ratio of their respective velocities is:

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