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

$A$ particle is moved along a path $A-B-C-D-E-F-A$,as shown in the figure,in the presence of a force $\vec{F} = (\alpha y \hat{i} + 2 \alpha x \hat{j}) \ N$,where $x$ and $y$ are in meters and $\alpha = -1 \ N/m$. The work done on the particle by this force $\vec{F}$ will be . . . . . . Joule.

The slope of the kinetic energy-displacement curve of a particle in motion is

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 ............... $J$.

$A$ force of $(5+3x) \text{ N}$ acts on a body of mass $20 \text{ kg}$ along the $x$-axis and displaces it from $x = 2 \text{ m}$ to $x = 6 \text{ m}$. The work done by the force is $.... \text{ J}$.

$A$ 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 $AFA$.