$A$ particle moves along the $x$-axis from $x = 0$ to $x = 5 \, m$ under the influence of a force $F$ (in $N$) given by $F = 3x^2 - 2x + 7$. Calculate the work done by this force in $J$.

The work done by a force $\vec{F} = (-6x^3 \hat{i}) \, N$ in displacing a particle from $x = 4 \, m$ to $x = -2 \, m$ is ............... $J$.

$A$ 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 $F$ acts on a particle,and its force-position curve is shown in the figure. The work done on the particle for a displacement from $0$ to $5\,m$ is ............. $J$.

$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

$A$ person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter,he gets progressively tired and his applied force reduces linearly with distance to $100\, N$. The total distance through which the box has been moved is $30\, m$. What is the work done by the person during the total movement of the box $........J$?