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

Suggest a suitable physical situation for the following $x-t$ graph.

The velocity $v$ of a particle is given by the equation $v = 6t^2 - 6t^3$,where $v$ is in $m/s$ and $t$ is time in $s$. Then:

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 velocity-time graph for a particle moving along the $x$-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by

Find the acceleration of the particle at $x = 5\,m$ using the given $v^2-x$ graph, where $v$ is velocity and $x$ is displacement.