The displacement-time graphs of two moving pa | vedclass

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

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$1: \sqrt{3}$

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(D) The velocity $v$ of a particle is given by the slope of the displacement-time graph,which is $v = 	an(	heta)$,where $	heta$ is the angle the graph makes with the time axis.For the first particle,$	heta_1 = 30^{\circ}$,so its velocity $v_1 = 	an(30^{\circ}) = \frac{1}{\sqrt{3}}$.For the second particle,$	heta_2 = 45^{\circ}$,so its velocity $v_2 = 	an(45^{\circ}) = 1$.The ratio of their velocities is $\frac{v_1}{v_2} = \frac{	an(30^{\circ})}{	an(45^{\circ})} = \frac{1/\sqrt{3}}{1} = 1 : \sqrt{3}$.

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

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