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

$A$ force is applied to a particle of mass $0.1 \ kg$ as a function of distance as shown in the figure. If it starts from rest at $x = 0$,its velocity at $x = 12 \ m$ is ....... $m/s$.

$A$ force acts on a $3.0 \ g$ particle in such a way that the position of the particle as a function of time is given by:
$x = 3t - 4t^2 + t^3$
Where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \ s$ is ................. $mJ$

The work done in displacing a particle from $y=a$ to $y=2a$ by a force $F = -\frac{K}{y^2}$ acting along the $y$-axis is:

What is a variable force? Write the equation for the work done by a variable force in one dimension.

$A$ particle is projected with velocity $v_{0}$ along the $x-$axis. $A$ damping force is acting on the particle which is proportional to the square of the distance from the origin,i.e.,$ma = -\alpha x^{2}$. The distance at which the particle stops is: