$A$ horizontal force $F = (g - x^2) \hat{i} \text{ N}$ acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from $x = 0$ to $x = 3 \text{ m}$ (in $\text{J}$) is (Use $g = 10 \text{ m/s}^2$)

An object starts from rest and is acted upon by a variable force $F$ as shown in the figure. If $-F_0$ is the initial value of the force at $x=0$,then the position of the object where it again comes to rest will be:

$A$ woman pushes a trunk on a railway platform which has a rough surface. She applies a force of $100 \; N$ over a distance of $10 \; m$. Thereafter,she gets progressively tired and her applied force reduces linearly with distance to $50 \; N$. The total distance through which the trunk has been moved is $20 \; m$. Plot the force applied by the woman and the frictional force,which is $50 \; N$ versus displacement. Calculate the work done by the two forces over $20 \; m$.

$A$ time-dependent force $F = 6t$ acts on a particle of mass $1 \ kg$. If the particle starts from rest,the work done by the force during the first $1 \ s$ will be ............... $J$.

$A$ force $F = \alpha + \beta x^2$ acts on an object in the $x$-direction. The work done by the force is $5 \ J$ when the object is displaced by $1 \ m$. If the constant $\alpha = 1 \ N$,then $\beta$ will be: (in $N/m^2$)

The area of the acceleration-displacement curve of a body gives