$A$ 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 $............. \, J$.

$A$ 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 $J$.

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 graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

$A$ bullet of mass $1 \ kg$ fired with a speed $2 \ m \ s^{-1}$ from $x = 0$ passes through a block of wood whose centre is kept at a distance of $10 \ m$ from the origin as shown in figure. The retarding force $F_r$ on the bullet within the wooden block is $-0.5/x$. The minimum length of the block (up to $1$ decimal digit) required to completely stop the bullet is (Assume $e^4 = 55$). (in $m$)

The work done in displacing a particle from $y=a$ to $y=2a$ by a force $F = -\frac{K}{y^2}$ acting along the $y$-axis is: