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:

Match Column-$I$ with Column-$II$:

$A$ train starting from rest travels the first part of its journey with constant acceleration $a$,the second part with constant velocity $v$,and the third part with constant retardation $a$,finally being brought to rest. The average speed for the whole journey is $\frac{7v}{8}$. The train travels with constant velocity for what fraction of the total time?

The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

The velocity-time graph of a body is shown in the figure. It implies that at point $B$