$A$ force of $(5+3x) \text{ N}$ acts on a body of mass $20 \text{ kg}$ along the $x$-axis and displaces it from $x = 2 \text{ m}$ to $x = 6 \text{ m}$. The work done by the force is $.... \text{ J}$.

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).

$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

$A$ 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?

$A$ block of mass $m=1 \; kg$ moving on a horizontal surface with speed $v_{i}=2 \; m \; s^{-1}$ enters a rough patch ranging from $x=0.10 \; m$ to $x=2.01 \; m$. The retarding force $F$ on the block in this range is inversely proportional to $x$ over this range,$F_{r} = -k/x$ for $0.1 < x < 2.01 \; m$,and $F_{r} = 0$ for $x < 0.1 \; m$ and $x > 2.01 \; m$,where $k=0.5 \; J$. What is the final kinetic energy $K_{f}$ and speed $v_{f}$ of the block as it crosses this patch?

$A$ particle of mass $500 \text{ g}$ is at rest. It is free to move along a straight line. The power delivered to the particle varies with time according to the following graph. The momentum of the particle at $t = 5 \text{ s}$ is