The displacement-time graph of two moving particles make angles of 30° and 45° with the X -axis. The ratio of their velocities is

In case x - t graph is a straight line, the slope of this line gives velocity of the particle. As slope = tan q, where q is the angle which the tangent to the curve makes with the horizontal in anti-clockwise direction. The velocities of two particles A and B are
${\mathrm{v}}_{\mathrm{A}}=\tan {30}^{\mathrm{o}}=\frac{1}{\sqrt{3}}$
v_B = tan 45° =1
The ratio of velocities,
${\mathrm{v}}_{\mathrm{A}} : {\mathrm{v}}_{\mathrm{B}}=\frac{1}{\sqrt{3}} : 1=1 : \sqrt{3}$