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

Consider a car initially at rest, starts to move along a straight road first with acceleration $5 \ m \ s^{-2}$, then with uniform velocity and finally, decelerating at $5 \ m \ s^{-2}$, before coming to a stop. Total time taken from start to end is $t = 25 \ s$. If the average velocity during that time is $72 \ km \ hr^{-1}$, the car moved with uniform velocity for a time of: (in $s$)

The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in the figure.
$(A)$ $A$ lives closer to the school.
$(B)$ $B$ lives closer to the school.
$(C)$ $A$ takes less time to reach home.
$(D)$ $A$ travels faster than $B$.
$(E)$ $B$ travels faster than $A$.
Choose the correct answer from the options given below:

The $v-t$ graphs of two moving objects make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. Find the ratio of their accelerations.

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_1$ to $t_2$?
$(a)$ $x(t_2) = x(t_1) + v(t_1)(t_2 - t_1) + (1/2)a(t_2 - t_1)^2$
$(b)$ $v(t_2) = v(t_1) + a(t_2 - t_1)$
$(c)$ $v_{\text{average}} = (x(t_2) - x(t_1)) / (t_2 - t_1)$
$(d)$ $a_{\text{average}} = (v(t_2) - v(t_1)) / (t_2 - t_1)$
$(e)$ $x(t_2) = x(t_1) + v_{\text{average}}(t_2 - t_1) + (1/2)a_{\text{average}}(t_2 - t_1)^2$
$(f)$ $x(t_2) - x(t_1) = \text{area under the } v-t \text{ curve bounded by the } t\text{-axis and the dotted lines shown.}$

The acceleration-time graph for a body is shown in the graph. Which of the following graphs would probably represent the velocity of the body plotted against time?