$A$ position-dependent force $F = (7 - 2x + 3x^2) \ N$ acts on a small object. The object is displaced from $x = 0$ to $x = 5 \ m$. What is the work done in Joules?

$A$ force $\vec F = k(y\hat i + x\hat j)$ where $k$ is a positive constant acts on a particle moving in the $x-y$ plane. The particle moves along a straight line from the point $(3, 5)$ to $(5, 7)$. The work done by the force is: ............... $k$

An object of mass $500 \; g$, initially at rest, is acted upon by a variable force whose $X$-component varies with $X$ as shown in the graph. The velocities of the object at $X = 8 \; m$ and $X = 12 \; m$ are, respectively:

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

$A$ 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 $m$)