In a one-dimensional case,the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $ergs$.

The graphs below show the magnitude of the force on a particle as the particle moves along the positive $x$ axis from the origin to $x = x_1$. The force is parallel to the $x$ axis and is conservative. The maximum magnitude $F_1$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force,from least (or most negative) to greatest (or most positive).

$A$ person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter,he gets progressively tired and his applied force reduces linearly with distance to $100\, N$. The total distance through which the box has been moved is $30\, m$. What is the work done by the person during the total movement of the box $........J$?

$A$ 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 $g = 10 \text{ m/s}^2$)

The force $F$ acting on a body varies with its position $x$ as shown in the figure. At which point is the body in unstable equilibrium?

Power applied to a particle varies with time as $P = (4t^3 - 5t + 2) \, W$,where $t$ is in seconds. Find the change in its $K.E.$ between time $t = 2 \, s$ and $t = 4 \, s$. ............... $J$