The displacement-time graph of two moving particles makes angles of $30^{\circ}$ and $45^{\circ}$ with the time axis ($X$-axis). The ratio of their velocities is

The displacement of a particle as a function of time is shown in the figure. The figure shows that

The position-time $(x-t)$ graphs for two children $A$ and $B$ returning from their school $O$ to their homes $P$ and $Q$ respectively are shown in the figure. Choose the correct entries in the brackets below:
$(a)$ $(A/B)$ lives closer to the school than $(B/A)$
$(b)$ $(A/B)$ starts from the school earlier than $(B/A)$
$(c)$ $(A/B)$ walks faster than $(B/A)$
$(d)$ $A$ and $B$ reach home at the (same/different) time
$(e)$ $(A/B)$ overtakes $(B/A)$ on the road (once/twice)

The $x-t$ equation is given as $x = 2t + 1$. The corresponding $v-t$ graph is:

The graph shows the variation of velocity of a rocket with time. The maximum height attained by the rocket is ........... $km$ :-

Velocity of a particle moving along a straight line is given by $v = t^2 - 3t - 4 \, (m/s)$. Find the velocity at the instant when no net force is applicable on the particle.......$m/s$ (in $.25$)