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 $x = 2 \ m$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance traversed by the particle in $m$ between $t=2\;s$ to $6\;s$.

$A$ particle shows a distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point:

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.

The figure shows $(v_x, t)$ and $(v_y, t)$ diagrams for a body of unit mass $(m = 1 \text{ kg})$. Find the force as a function of time.

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.