$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in newton $(N)$ and $x$ is in metre $(m)$. The work done by the force in moving the object from $x = 0$ to $x = 6\,m$ 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 graph of the resistive force acting on an object versus the distance covered by it is shown in the figure. The mass of the object is $2 \ kg$ and its initial velocity is $10 \ m/s$. When the distance covered by the object is $4 \ m$,its kinetic energy will be $.... \ J$. (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 ............... $J$.

$A$ 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 $J$.

$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in $N$ and $x$ is in $m$. The work done by the force in moving the object from $x = 0$ to $x = 6$ is ............. $J$.