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

The potential energy $U(x)$ of a system is represented in the figure. The force $F(x)$ acting on the system will be represented by:

For a particle moving under the action of a variable force,the kinetic energy-position $(K-x)$ graph is given. Then:

$A$ force $\overrightarrow{F} = (2 + 3x) \hat{i}$ acts on a particle in the $x$ direction,where $F$ is in newton $(N)$ and $x$ is in meter $(m)$. The work done by this force during a displacement from $x = 0$ to $x = 4 \, m$ is ....... $J$.

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20 \, m$ is (in $ \, J$)

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