The graph of resistive force versus displacement for an object of mass $25 \ kg$ is given. If its velocity at $x = 0$ is $2 \ m/s$,then its kinetic energy at $x = 4 \ m$ is ..... $J$.

An object of mass '$m$' initially at rest on a smooth horizontal plane starts moving under the action of a force $F = 2 \text{ N}$. In the process of its linear motion,the angle $\theta$ (as shown in the figure) between the direction of the force and the horizontal varies as $\theta = kx$,where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression for the kinetic energy of the object is $E = \frac{n}{k} \sin \theta$. The value of $n$ is .....

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the work done by the normal reaction $N$ between the block and the spring on the block is

The figure shows the $F-x$ graph,where $F$ is the force applied and $x$ is the distance covered by the body along a straight-line path. Given that $F$ is in newton $(N)$ and $x$ is in metre $(m)$,calculate the total work done in joules $(J)$.

$A$ particle moves along the $x$-axis from $x = 0$ to $x = 5 \, m$ under the influence of a force $F$ (in $N$) given by $F = 3x^2 - 2x + 7$. Calculate the work done by this force in $J$.

$A$ 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).