$A$ position-dependent force $F$ acts on a particle,and its force-position curve is shown in the figure. The work done on the particle for a displacement from $0$ to $5\,m$ is ............. $J$.

The slope of the kinetic energy-displacement curve of a particle in motion is

$A$ force $\vec{F} = x^2 y \hat{i} + y^2 \hat{j}$ acts on a particle in a plane $x + y = 10$. The work done by this force during a displacement from $(0, 0)$ to $(4 \ m, 2 \ m)$ is . . . . . . $Joule$ (round off to the nearest integer).

$A$ woman pushes a trunk on a railway platform which has a rough surface. She applies a force of $100 \; N$ over a distance of $10 \; m$. Thereafter,she gets progressively tired and her applied force reduces linearly with distance to $50 \; N$. The total distance through which the trunk has been moved is $20 \; m$. Plot the force applied by the woman and the frictional force,which is $50 \; N$ versus displacement. Calculate the work done by the two forces over $20 \; m$.

$A$ particle of mass $0.1 \, kg$ is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at $x = 0$,its velocity at $x = 12 \, m$ is .......... $m/s$.

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