The relationship between force $F$ and displacement $x$ is shown in the figure. The work done by the object for a displacement from $x = 1 \ m$ to $x = 5 \ m$ is equal to ... $J$.

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

$A$ force $(3x^2 + 2x - 5) \text{ N}$ displaces a body from $x = 2 \text{ m}$ to $x = 4 \text{ m}$. The work done by this force is .......... $J$.

The value of the force constant for the given force-displacement graph is:

$A$ point particle of mass $0.5 \ kg$ is moving along the $x-$ axis under a force described by the potential energy $V$ shown in the graph. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin? (in $ms^{-1}$)

The graph of resistive force versus displacement for an object of mass $25 \ kg$ is given. If its velocity at $x = 0$ is $2 \ m/s$,then its kinetic energy at $x = 4 \ m$ is ..... $J$.