$A$ force $F = \alpha + \beta x^2$ acts on an object in the $x$-direction. The work done by the force is $5 \ J$ when the object is displaced by $1 \ m$. If the constant $\alpha = 1 \ N$,then $\beta$ will be: (in $N/m^2$)

The force $F$ acting on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12\, m$ is ................. $J$.

Consider a force $F = Kx^3$, which acts on a particle at rest. The work done by the force for a displacement of $2 \,m$ is given that $K = 2 \,N \cdot m^{-3}$. (in $\,J$)

$A$ 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 relationship between force and position is shown in the figure given (in one-dimensional case). The work done by the force in displacing a body from $x = 1 \, cm$ to $x = 5 \, cm$ is .......... $ergs$.

The figure shows the $F-x$ graph,where $F$ is the force applied and $x$ is the distance covered by the body along a straight-line path. Given that $F$ is in newton $(N)$ and $x$ is in metre $(m)$,calculate the total work done in joules $(J)$.