When a rubber band is stretched by a distance $x$,it exerts a restoring force of magnitude $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

The force $F$ acting on a body varies with its position $x$ as shown in the figure. At which point is the body in unstable equilibrium?

$A$ block of mass $2\,kg$ moving on a horizontal surface with speed of $4\,ms^{-1}$ enters a rough surface ranging from $x = 0.5\,m$ to $x = 1.5\,m$. The retarding force in this range of rough surface is related to distance by $F = -kx$ where $k = 12\,Nm^{-1}$. The speed of the block as it just crosses the rough surface will be ........... $ms^{-1}$.

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 $AFA$.

$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.