A force varies as \(F_x=5x\). Find the work done from \(x=0\) to \(x=2.0\,\mathrm{m}\).

On a force-position graph, what does the signed area under the \(F_x\) curve represent?

A force-position graph is a triangle with base \(3.0\,\mathrm{m}\) and height \(12\,\mathrm{N}\), entirely above the axis. Find the work.

A spring has \(k=100\,\mathrm{N\,m^{-1}}\). Find the work done by the spring as it moves from \(x=0.20\,\mathrm{m}\) to \(x=0\).

A force is \(F_x=6-2x\) in newtons. Find the work from \(x=0\) to \(x=4.0\,\mathrm{m}\).

A force is \(F_x=3x^2\) in newtons. Find the work from \(x=1.0\,\mathrm{m}\) to \(x=3.0\,\mathrm{m}\).

A graph of \(F_x\) against \(x\) is a rectangle at \(8\,\mathrm{N}\) from \(x=0\) to \(x=2\,\mathrm{m}\), followed by a triangle from \(8\,\mathrm{N}\) down to \(0\) between \(x=2\) and \(x=5\,\mathrm{m}\). Find the work.

A force is \(F_x=10-4x\) in newtons. Find the work from \(x=0\) to \(x=5.0\,\mathrm{m}\), keeping the sign.

A spring has \(k=250\,\mathrm{N\,m^{-1}}\). Find the work done by an external force that slowly stretches it from \(x=0\) to \(x=0.12\,\mathrm{m}\).

A force is \(F_x=ax\). If it does \(24\,\mathrm{J}\) of work from \(x=0\) to \(x=4.0\,\mathrm{m}\), find \(a\).

A force is \(F_x=4x-12\). Find the work from \(x=0\) to \(x=5.0\,\mathrm{m}\), state whether the force adds or removes kinetic energy overall, and find the location where the force changes from removing to adding energy.

A \(2.0\,\mathrm{kg}\) object starts from rest at \(x=0\). A force \(F_x=6x\) acts from \(x=0\) to \(x=3.0\,\mathrm{m}\). Find the final speed.

A \(1.0\,\mathrm{kg}\) object starts at \(x=0\) with speed \(2.0\,\mathrm{m\,s^{-1}}\). A force \(F_x=9-3x\) acts until \(x=4.0\,\mathrm{m}\). Find the speed at \(x=4.0\,\mathrm{m}\), then find the maximum speed reached in \(0\le x\le4\).

A spring force is \(F_x=-kx\). Starting from the integral definition of work, derive the work done by the spring from \(x_i\) to \(x_f\), then state the sign of work for (i) stretching further and (ii) relaxing toward equilibrium.

A \(1.0\,\mathrm{kg}\) particle starts at \(x=0\) with speed \(3.0\,\mathrm{m\,s^{-1}}\). A force \(F_x=8-4x\) acts. Find all turning positions and classify the first one reached for motion initially toward +x.

A force-position graph has \(F_x=6\,\mathrm{N}\) from \(x=0\) to \(2\,\mathrm{m}\), then decreases linearly to \(-6\,\mathrm{N}\) at \(x=6\,\mathrm{m}\). A \(2.0\,\mathrm{kg}\) object starts at \(x=0\) with speed \(4.0\,\mathrm{m\,s^{-1}}\). Find its speed at \(x=6\,\mathrm{m}\), then determine whether it can continue past \(x=6\) if \(F_x=-6\,\mathrm N\) remains constant beyond that point.