The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point:

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

The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance (in $m$) traversed by the particle between $t=0\; s$ and $t=10\; s$.

The velocity of a particle moving on the $x$-axis is given by $v = x^2 + x$,where $v$ is in $m/s$ and $x$ is in $m$. Find its acceleration in $m/s^2$ when passing through the point $x = 2 \ m$.

$A$ car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ seconds,the total distance travelled is

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. Find the displacement of the particle in $m$ when its velocity becomes zero.