$A$ particle moves along the $X$-axis from $x=0$ to $x=1 \, m$ under the influence of a force given by $F=3x^2+2x-10$. The work done in the process is ............. $J$.

$A$ 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?

The graph between power $(P)$ and time $(t)$ is given below. Which of the following options is correct for the work done by the force [from $t = 0$ to time $t$]?

$A$ body of mass $3 \ kg$ moves under the influence of a force such that its displacement is given by $s = t^3/3 \ m$. What is the work done by the force in the first $2 \ s$ in $J$?

The potential energy $U(x)$ of a system is represented in the figure. The force $F(x)$ acting on the system will be represented by:

Consider a force $F = Kx^3$, which acts on a particle at rest. The work done by the force for a displacement of $2 \,m$ is given that $K = 2 \,N \cdot m^{-3}$. (in $\,J$)