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

$A$ block of mass $1 \ kg$,moving along the $x$-axis with an initial speed $v_{i} = 10 \ m/s$,enters a rough region ranging from $x = 0.1 \ m$ to $x = 1.9 \ m$. The retarding force acting on the block in this range is $F_{r} = -kx \ N$,where $k = 10 \ N/m$. Find the final speed of the block as it crosses the rough region.

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

$A$ point particle of mass $0.5 \ kg$ is moving along the $x-$ axis under a force described by the potential energy $V$ shown in the graph. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin? (in $ms^{-1}$)

The adjacent figure shows the force-displacement graph of a moving body. The work done in displacing the body from $x = 0$ to $x = 35\,m$ is equal to ........... $J$.

The adjacent figure shows the force-displacement graph of a moving body. What is the work done by this force in displacing the body from $x = 0$ to $x = 35\,m$ (in $,J$)?