$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ 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 .....

$A$ position-dependent force $F = 7 - 2x + 3x^2 \, N$ acts on a small body of mass $2 \, kg$ and displaces it from $x = 0$ to $x = 5 \, m$. The work done in joules is

$A$ body of mass $8\,kg$ is moved by a force $F = 3x\,N$,where $x$ is the distance covered. The initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s$. The final speed is ........... $m/s$.

What will be the area under the graph of variable force versus position?

The figure shows the variation of a force $F$ acting on a particle along the $x$-axis. If the particle begins at rest at $x=0$,what is the particle's coordinate when it again has zero speed?