$A$ block of mass $10 \, kg$,moving in $x$ direction with a constant speed of $10 \, m/s$,is subjected to a retarding force $F = 0.1 \, x \, N$ during its travel from $x = 20 \, m$ to $30 \, m$. Its final $KE$ will be ............... $J$.

$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in newton $(N)$ and $x$ is in metre $(m)$. The work done by the force in moving the object from $x = 0$ to $x = 6\,m$ is......$J$.

$A$ 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 ............. $J$.

$A$ 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: ............... $k$

The work done on a particle of mass $m$ by a force,$F = K \left[ \frac{x}{(x^2+y^2)^{3/2}} \hat{i} + \frac{y}{(x^2+y^2)^{3/2}} \hat{j} \right]$ (where $K$ is a constant of appropriate dimensions),when the particle is moved from the point $(a, 0)$ to the point $(0, a)$ along a circular path of radius $a$ about the origin in the $x-y$ plane is:

$A$ force $\vec{F} = (7 - 2x + 3x^2) \, N$ is applied to an object. Calculate the work done as the object moves from $x = 0$ to $x = 5 \, m$. (in $, J$)