The relationship between force and position is shown in the figure given (in one-dimensional case). The work done by the force in displacing a body from $x = 1 \, cm$ to $x = 5 \, cm$ is .......... $ergs$.

The force $F$ acting on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12\, m$ is ................. $J$.

$A$ sphere of mass $m$ is set in motion with initial velocity $v_0$ on a surface where $kx^n$ is the frictional force,with $k$ and $n$ as constants and $x$ as the distance from the starting point. Find the distance at which the sphere will stop.

Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

What will be the area under the graph of variable force versus position?

$A$ $1 \,kg$ box placed at the origin starts sliding along the $x$-axis under the action of a force $\vec{F} = F \hat{i}$. Its acceleration as a function of $x$ is given by $a(x) = \beta x$,where $\beta = 5 \,s^{-2}$. The work done by $\vec{F}$ in moving the box from $x = 2 \,cm$ to $x = 5 \,cm$ in joules is: