When a force $\vec{F} = (17 - 2x + 6x^2) \text{ N}$ acts on a body of mass $2 \text{ kg}$ and displaces it from $x = 0 \text{ m}$ to $x = 8 \text{ m}$,the work done is: (in $\text{ J}$)

$A$ body of $0.5 \,kg$ moves along the positive $X$-axis under the influence of a varying force $F$ (in newton) as shown below. If the speed of the object at $x=4 \,m$ is $3.16 \,ms^{-1}$,then its speed at $x=8 \,m$ is ................. $\,ms^{-1}$.

$A$ 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.

Obtain the equation of work done by a variable force in one dimension.

$A$ body of mass $200\,g$ is moving along the $XY$ plane. The work performed by the force given by $\vec F = (2x\hat i + y\hat j)$ acting on it when the body is displaced from $(0, 0)$ to $(1, 2)$ will be equal to ............... $unit$.

The adjacent figure shows the force-displacement graph of a moving body. The work done in displacing the body from $x = 0$ to $x = 35\,m$ is equal to ........... $J$.