The acceleration-displacement graph of a $10 \ kg$ particle is given. Find the work done as the particle moves from $x = 0 \ cm$ to $x = 8 \ cm$.

$A$ 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 $J$?

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

$A$ particle experiences a variable force $\overrightarrow{F} = (4x \hat{i} + 3y^2 \hat{j})$ in a horizontal $x-y$ plane. Assume distance is in meters and force is in newtons. If the particle moves from point $(1, 2)$ to point $(2, 3)$ in the $x-y$ plane,the kinetic energy changes by............$J$.

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 .....

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