Physical meanings of kinetic energy While studying energy on Sears & Zemansky's University Physics, I came up with a doubt on the meaning of kinetic energy. The book gives two possible physical interpretations of this quantity.

So the kinetic energy of a particle is equal to the total work that was done to accelerate it from rest to its present speed [...] The kinetic energy of a particle is equal to the total work that particle can do in the process of being brought to rest.

I'm okay with the first meaning of KE but I don't understand completely the second one. How can the particle do work?
If we take a ball with velocity $v$ that meets a spring, the spring is compressed and the ball is stopped. But here it's the spring that does work on the ball, or vice-versa? The ball gains potential energy ($W_\textrm{spring}=-\Delta U_\textrm{ball}$) and mechanical energy is conserved in the process. Nevertheless I do not see if and where the ball does work here.
 A: I would say the system gains the potential energy in that example.  The ball does work on the spring equal to the ball's initial kinetic energy.
Consider the direction of the force and displacement of each.  The force the ball applies on the spring and the balls displacement as it applies it are in the the same direction so the work done is positive - it transfers energy to the spring & ball system.  The spring's displacement and the force it applies on the ball are in opposite directions so the work it does on the ball is negative - the ball loses energy.
A: "How can the particle do work?" Unless the particle was applying a force on a mass through some distance, the particle doesn't do any work. Work is done by a force through some displacement in the direction of the force.
Work is done in bringing that particle to rest by some acceleration through some displacement, sure. The wording is poor, but the meaning is essentially the same.
In your example, the spring does the work on the ball (Which is negative, btw), because the spring exerts a force on the ball through the displacement. 
edit: The poster above me is more correct actually. You can describe it both ways because of Newton's 3rd Law. KE is the amount of work done to bring an object to rest, or the amount of work the particle can do before coming to rest. 
