$A$ block of mass $2 \ kg$ is initially at rest on a horizontal frictionless surface. $A$ horizontal force $\overrightarrow{F} = (9 - x^2) \hat{i} \ N$ acts on it, starting from $x = 0$. The maximum kinetic energy of the block between $x = 0$ and $x = 3 \ m$ in joules is:

$A$ force acts on a particle moving along the $x$-axis,and its variation with position is shown in the figure. At which point will the particle be in a stable equilibrium position?

$A$ force $(3x^2 + 2x - 5) \text{ N}$ displaces a body from $x = 2 \text{ m}$ to $x = 4 \text{ m}$. The work done by this force is .......... $J$.

$A$ particle moves along the $x$-axis from $x=0$ to $x=5 \ m$ under the influence of a force $F = 7 - 2x + 3x^2$. The work done in the process is ............. (in $J$)

$A$ block of mass $2\,kg$ moving on a horizontal surface with speed of $4\,ms^{-1}$ enters a rough surface ranging from $x = 0.5\,m$ to $x = 1.5\,m$. The retarding force in this range of rough surface is related to distance by $F = -kx$ where $k = 12\,Nm^{-1}$. The speed of the block as it just crosses the rough surface will be ........... $ms^{-1}$.

The graph between power $(P)$ and time $(t)$ is given below. Which of the following options is correct for the work done by the force [from $t = 0$ to time $t$]?