Consider a force $\overrightarrow{F}=-x \hat{i}+y \hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is (all quantities are in $SI$ units).

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

$A$ force $F = (5 + 3y^2)$ acts on a particle in the $y$ direction,where $F$ is in newtons and $y$ is in meters. The work done by the force during a displacement from $y = 2 \, m$ to $y = 5 \, m$ is $............. \, J$.

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 $(J)$.

$A$ 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 ........... $ms^{-1}$.

$A$ particle moves along the $x$-axis from $x = 0$ to $x = 10 \ m$ under the influence of a force $\vec{F}(x) = (3x^2 - 2x + 7) \hat{i} \ N$. The work done during this displacement is ........ $J$.