The work done by a force $\vec F = (-6x^3\hat i)\, N$,in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $J$.

$A$ 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 $, J$)

$A$ particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x = 0$ has a kinetic energy of $25\,J$,then the kinetic energy of the particle at $x = 16\,m$ is .............. $J$.

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to force $|\vec{F}|=\frac{mg}{9}$. The magnitude of the force remains constant with time. The force vector makes an angle $\theta$ with the horizontal which varies with the distance covered as $\theta= Cx$. If the constant $C=10 \text{ degree/meter}$, then the speed of the bar, when $\theta$ becomes equal to $30^{\circ}$ for the first time, is (Assume $g = 10 \text{ m s}^{-2}$) (in $\text{ m s}^{-1}$)

$A$ sphere of mass $m$ is set in motion with initial velocity $v_0$ on a surface where $kx^n$ is the frictional force,with $k$ and $n$ as constants and $x$ as the distance from the starting point. Find the distance at which the sphere will stop.

Consider a force $F = Kx^3$, which acts on a particle at rest. The work done by the force for a displacement of $2 \,m$ is given that $K = 2 \,N \cdot m^{-3}$. (in $\,J$)