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 $\text{ J}$)

The force $F$ acting on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12\, m$ is ................. $J$.

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

$A$ $1 \,kg$ box placed at the origin starts sliding along the $x$-axis under the action of a force $\vec{F} = F \hat{i}$. Its acceleration as a function of $x$ is given by $a(x) = \beta x$,where $\beta = 5 \,s^{-2}$. The work done by $\vec{F}$ in moving the box from $x = 2 \,cm$ to $x = 5 \,cm$ in joules is:

The work done by a force $\vec{F} = -5x^4 \hat{i} \text{ N}$ in displacing a body from $x = 2 \text{ m}$ to $x = -2 \text{ m}$ is: (in $\text{ J}$)