Question

A 40.0-kg solid cylinder is rolling across a horizontal surface at a speed of 6.0 m/s. how much work is required to stop it

Answer 1

One way of thinking of energy is to say the energy is the ability of the body to do work. If you have a body that is moving that body has kinetic energy, as said above this energy can be used to do work. The amount of work done is equal to the amount of energy that body has.
In our case cylinder has the following kinetic energy:
$E_k=m\frac{v^2}{2}\\ E_k=40\frac{6^2}{2}\\ E_k=40\cdot18\\ E_k=720 J$
And that is exaclty how much work you would have to put in to stop the cylinder.