$A$ block of mass $10\,kg$ is moving along the $x$-axis under the action of a force $F = 5x\,N$. The work done by the force in moving the block from $x = 2\,m$ to $4\,m$ will be ............$J$.

$A$ particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled $3\, m$ is ................ $J$.

$A$ horizontal force $F = (g - x^2) \hat{i} \text{ N}$ acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from $x = 0$ to $x = 3 \text{ m}$ (in $\text{J}$) is (Use $g = 10 \text{ m/s}^2$)

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 $t$]?

$A$ particle of mass $10\,g$ moves in a straight line with retardation $2x$,where $x$ is the displacement in $SI$ units. Its loss of kinetic energy for the above displacement is $\left(\frac{10}{x}\right)^{-n}\,J$. The value of $n$ will be $............$.

$A$ person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter,he gets progressively tired and his applied force reduces linearly with distance to $100\, N$. The total distance through which the box has been moved is $30\, m$. What is the work done by the person during the total movement of the box $........J$?