91Ó°ÊÓ

In physics, a conservative force is any force that only affects the eventual displacement of the item it acts upon, such as the gravitational force between the Earth and another mass. The total work performed by a conservative force is equal to zero when the path is a closed loop and is independent of the path leading to a specific displacement.

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis.

Also we have given the graph of potential energy function versus\(x\).

Here given graph is of potential energy versus\(x\).

Initially, the particle was at rest, so the force can only act in the direction of velocity.

Here at point\(A\), the potential energy decreases in positive x-direction.

Which means that the initial force is acting in positive x-direction when particle is on point \(A\)

Here given graph is of potential energy versus\(x\).

Here at point\(B\), the potential energy increases in negative x-direction

Which means that the initial force is acting in negative x-direction when particle is on point \(B\)

Here given graph is of potential energy versus\(x\).

We know that if at any point potential energy is minimum, the kinetic energy is maximum.

Here in given graph we can see that at\(x \approx 0.7\), the potential energy is minimum.

Hence at \(x \approx 0.7\), the kinetic energy is maximum.

Here given graph is of potential energy versus\(x\).

Here at point\(C\), we can see that rate of change of potential energy is 0.

Hence the force at point \(C\) is 0.

Here given graph is of potential energy versus\(x\).

Here in the graph, we can see that the maximum value of\(x\)is \(x \approx 2.1\).

Hence the largest value of \(x\) reached by the particle during its motion is \(x \approx 2.1\)

Here given graph is of potential energy versus\(x\).

We know that stable equilibrium occurs at point of local minima.

Here in given graph we can see that local minima occur at\(x \approx 0.7,\;1.7\).

So, the values of \(x\) corresponds to points of stable equilibrium is \(x \approx 0.7,\;1.7\).

Here given graph is of potential energy versus\(x\).

We know that unstable equilibrium occurs at the point of local maxima.

Here in given graph we can see that local maxima occur at\(x \approx 1.4\).

So, the values of \(x\) corresponds to points of stable equilibrium is \(x \approx 1.4\).