$A$ force of $(5+3x) \text{ N}$ acts on a body of mass $20 \text{ kg}$ along the $x$-axis and displaces it from $x = 2 \text{ m}$ to $x = 6 \text{ m}$. The work done by the force is $.... \text{ J}$.

$A$ force $\vec{F} = (-6x^3 \hat{i}) \ N$ acts on a particle,causing a displacement from $x = 4 \ m$ to $x = -2 \ m$. The work done by the force is .......... $J$.

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20 \, m$ is (in $ \, J$)

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).

$A$ 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 $ms^{-1}$)

$A$ particle moves along the $x$-axis from $x = 0$ to $x = 5 \, m$ under the influence of a force $F$ (in $N$) given by $F = 3x^2 - 2x + 7$. Calculate the work done by this force in $J$.