The displacement-time graphs of two moving particles make angles of $30^\circ$ and $45^\circ$ with the x-axis

Question

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

Accepted Answer

The slope of a displacement-time graph gives the velocity. Therefore, the ratio of velocities is $\frac{v_1}{v_2} = \frac{	an 30^\circ}{	an 45^\circ} = \frac{1/\sqrt{3}}{1} = 1 : \sqrt{3}$.

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