$A$ body of mass $3\, kg$ is under a force,which causes a displacement given by $S = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first $2\, s$.

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by the graph shown in the figure. If the object undergoes a displacement from $X = 0.5 \, m$ to $X = 2.5 \, m$,the work done will be approximately equal to .............. $J$.

$A$ graph of potential energy $V(x)$ versus $x$ is shown in the figure. $A$ particle of energy $E_0$ is executing motion in it. Draw the graph of velocity and kinetic energy versus $x$ for one complete cycle $AFA$.

$A$ position-dependent force $F = 7 - 2x + 3x^2 \, N$ acts on a small body of mass $2 \, kg$ and displaces it from $x = 0$ to $x = 5 \, m$. The work done in joules is

$A$ particle moves along the $X$-axis from $x=0$ to $x=1 \, m$ under the influence of a force given by $F=3x^2+2x-10$. The work done in the process is ............. $J$.

$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.