Thanks for your answer to my kinetic energy question.I still would like to know how the ball initially at rest can "jump" to some velocity,it is a similar problem to Zeno's paradox but I still cannot see how the ball can go from no velocity to some velocity.PS.is a "free particle" one that is in equilibrium? if so the ball in question is not a free particle and it's it's kinetic energy that I was referring to.
Let me answer this by not actually answering your question.
I have an issue that bugs me, that is connected with it...
Suppose I lift a box. Let us consider that the box is rigid, totally.
I lift the box. I am separating it from the earth. When one separates attracting bodies, the one can think of it as giving the system some amount of potential energy.
But there is a subtle issue here. Note that I cannot give a system potential energy unless I HAD PREVIOUSLY given it some kinetic energy: you cannot separate two bodies without giving them a certain speed! (at least not in the world of pots and pans). You simply cannot....
This is the same as to say that the Force that is lifting the box up (separating it from the earth), the same force that is equalized by the so called force of gravity, does NO WORK unless there HAD been another UNBALANCED force that has given this body a small kick of an acceleration. Now the body has a constant speed and the force that is lifting the box, the same force which is being balanced by the gravity, SUDDENLY is able to do some work!
I find it kooky, bizarre. One might say that there is nothing strange about it...bla bla.. but it sort of is strange...
It seems to give rise to the idea, that one needs to give a system an extra kick to let other forces do some work...
Like in order to light a match, one has to invest a tiny amount of energy to get this process going...
Like it is with chemical reactions (which also involve physical work).
Like it is with proton fusion in stars: a slight amount of energy is needed in order to get a process going that releases MORE energy..
There are some similarities between those example, except that in the case of lifting the box, there is no energy actually released.
This idea also fits with the equation describing physical POWER:
POWER = FORCE x SPEED
If the speed of the body is 0, there is no power, no work done.
So if I wanted to hide behind the math, I would say: shut up and don't complain: you see the equation: it does give 0 work since it is zero power. So everything is ok, mathematics explains everything.. huh...
But there is something bizarre about it. A body's speed somehow seems to contribute to a balanced force's ability to do work.
On the other hand it makes sort of sense if we consider that one cannot separate the two bodies unless you give them at least a little speed.