$A$ body of mass $2.4 \, kg$ is subjected to a force which varies with distance as shown in the figure. The body starts from rest at $x=0$. Its velocity at $x=9 \, m$ is

$A$ 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?

What is a variable force? Write the equation for the work done by a variable force in one dimension.

$A$ force $\vec{F} = (-6x^3 \hat{i}) \ N$ acts on a particle,causing a displacement from $x = 4 \ m$ to $x = -2 \ m$. The work done by the force is .......... $J$.

$A$ 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 $.... \text{ J}$.

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 $J$)