Can a human size object move so fast that it ceases to be observable? In many anime, comics, movies, etc, we see a lot of super human beings moving and fighting at such high speeds that a regular human being cannot see that they are fighting or moving pass by.
In particular, in the first battle between Goku and Piccolo, those two are able to fight in a confined environment (when Piccolo first appears in the comics, stage fight, if I remembered correctly), and regular audiences are unable to see them when they battle. 
Is it physically possible for a "human" (human size object) to move in a confined environment (let's say, $20~\text{m} \times 20~\text{m} \times 10~\text{m}$ ) so fast that a normal person would be unable to see it? If it is possible, how fast must this "person" be?
Assume that this "human" cannot move faster than, or even close to the speed of light.
Some clarifications:
First, please ignore the strength/physicality of the object, and consider it an object that can can move "freely" in this confined space without causing any "side effects" (such as heat, sounds, etc)
Second, please take in note that the object is moving in a confined, rather small 3D space as mentioned in the question, and the observer would be always able to see the entire space. 
And last, a blurred image would be considered as "able to see". 
 A: Curiously, there was a paper about a decade ago that covered this topic. From the abstract, they moved an object

within a wide speed range (0.4-500 degrees /sec) and compared these with human reaction times (RTs). 

They showed response times on the order of a few hundred milliseconds finding also that the response time was inversely related to the motional speed (i.e., the faster it went the smaller the response time). I believe there was a recent study (cannot find it at the moment) in which response times were under 100 ms for some stimuli (it wasn't tracking movement).
Extrapolating from this, the superhuman would have to move at over 10$^3$ degrees/second over very short distances for the movement to be impossible to see. Since Goku & Piccolo are fighting, hand motions are going too far for the fight to be invisible at any speed (as Jim right points out, the image observed would be rather blurry).
A: The accepted answer is clearly wrong.  Lets look at a real world approximation of the situation:
A standard technique to remove people from a scene is to take a long exposure shot (you'll need a high level neutral density filter to do this), presto--the scenery with no people.
This works because the people move around enough that they are averaged out, merely tinting the areas they frequent a bit.  (Note that this will fail if someone is sitting still in the frame, they'll still be there although blurred.)
Here is an article about it, complete with images.  Note the missing tourists.  Note that the camera is set for a 15 second time exposure.
I don't know the maximum image rate of the human eye but I do know that we typically consider 60Hz enough for smooth motion.  I'll be generous and take that up to 100Hz.
Thus lets speed up our tourist removal by 1500x.  Humans typically walk about 3 miles per hour so we need to raise this to 4500 miles per hour.  This is a miniscule fraction of lightspeed, the no-relativistic requirement is satisfied.
Note that it is not required for the target to leave the observation area, they merely must move to many places within it so their image is spread over so much space you can't see it.
While we are talking extreme G forces (approaching that of a bullet being fired), extreme heating and the mother of all sonic booms we have an invisible creature in front of us.
A: While magicians sometimes use very fast hand motions, they are still visible. And the magicians usually try to keep the attention away from what they're doing.
If you were to think of the human eye as a video camera, it would take about 1000 frames per second (I believe). So anything you do, would have to take less than 1/1000th of second to complete. As it is, I know of nothing organic (flora or fauna) that can move with this speed.
Actually, the conduction speed for a neuron would not let a human move that fast. The conduction velocity of a nerve (how fast it tells the muscle to move the hand off the stove) is up to 120 m/s. In many cases (like the hand on the stove one) the brain is not involved in moving the muscle way from something damaging (like a hot stovetop) until after the fact. The nerve signal actually gets processed in your spinal cord (to avoid waiting those extra milliseconds that it would take to get the brain involved).
Humans can become several times stronger when faced with danger of various types. This is where you get the stories of mothers lifting cars of their children, etc. While this is possible, it can (and does to some degree) damage your body extensively. (Getting hernias, breaking weight bearing bones, etc.) But because of neurotransmitters that block pain receptors being released, you would not feel it.
In short, humans can't be super fast. (Dang!)
In a little longer sentence, humans can't be super fast, because their muscles would shred, and their nerves aren't fast enough. (Double Dang!)
I hope this helps answer your question. This answer is kind of disappointing though. (I think everyone wants to be as fast as Superman.)
Nerve reaction time
Super strength in humans
Edit: Huh. The answer by Jim says the eye framerate is 30 fps... I'm going to go find my source for the framerate of the human eye.
A: Let me start by clarifying that I assume the question is whether a superhuman or any object of human size can render itself invisible through speed alone. And that the speed of said object must be $v\ll c$. From this, I assume that the object or person being viewed must spend a reasonably long amount of time within the observer's field of view such that invisibility can't be cheated through exploiting blinks or by having too short an exposure time or by hiding behind the observer most of the time.
In short, no, it is not possible for something to move fast enough that a normal human would cease to see it entirely. Firstly, at any velocity, the amount of light that is redirected from the moving object to the observer is reasonably constant. At relativistic velocities, length contraction of the moving object in the observer's frame could reduce the size and, thus, visibility of the object; however, the previously mentioned speed restriction allows us to ignore any contraction of this magnitude. Additionally, the human eye-brain system processes input continuously and uses as-yet not completely understood processes for extrapolating and interpolating motion. In fact, even when presented with rapid images of the same object at different locations, the brain has the ability to assume motion and perceives these images as being continuously linked; something referred to as stroboscopic motion or illusory motion of stroboscopic images. Since the objects moving quickly still have light shining on them, the light that reflects towards the observer would still be captured and processed. However, since image processing is a complex task and due to something called persistence of vision, the images we perceive can include not only the light that recently entered your eyes, but also parts of previously perceived images. Therefore, at higher speeds, the image an observer gets would probably be blurry as it is an amalgamation of the moving object's position at multiple times as well as an effect of small eye movements; this is sometimes called motion blur.
However, while it is not possible to disappear entirely, there are other and cooler things that are possible. Because of the processing speed of the eye-brain system and the illusory effects that can be created from the brain's extrapolation of data, it is entirely possible for an object to move fast enough that it does not appear to move at all. If Goku and Piccolo fight each other at an extremely high speed, but they make sure to periodically spend most of every, say, second in one specific position, then the images your eye captures will be mostly of them in those specific positions. As a result, they will appear unmoving to an observer (except, of course, for mysterious cuts and bruises showing up and their edges may appear slightly more blurred). Additionally, by spending an equal amount of time in two different locations (and with the help of perfect timing) it can appear as if there is two identical and slightly faded/blurry copies of the moving object. This effect works for creating large numbers of copies and can also be used to make the image appear to "jump" from place to place.
Some have argued that an extremely fast moving object can blur so much as to be indistinguishable from the background. This may be true, however it is more dependent on the contrast between the background and the object than on purely its speed. Once camouflage and things of that sort are ruled out, there is simply no non-relativistic speed where a human-sized object in a confined space can become invisible to an ideal, normal human observer for an extended period of time.
Let me further add that at relativistic speeds, it's possible for the light reflecting off the moving object to be red or blue-shifted outside of the visible spectrum (although, in the case of blue-shifting, the object's own heat, ie IR emissions, would be shifted into the visible range). This could make the object invisible (and would be really cool to see happening), but as the question requires speeds "[not] even close to the speed of light", that rules out the possibility in this case. Additionally, since it is in a confined environment and the red-shifting effect only works for when the object is travelling away from the observer, the invisibility effect would not last long enough to be considered sustainably invisible.
A: Obviously, it is theoretically possible for something to move so fast that you hardly notice it. The second part, about "confined space" implies that it must also be able to accelerate and decelerate very fast as well.
An example of a real-world object that moves in a confined space and is barely visible is an aircraft propellor. It seems from Aviation Stack Exchange question Where to find tach hour and clock hour equivalence RPM? that 2400 rpm = 40 rev/s is a fairly normal prop speed, giving a tip velocity for a 1 m radius propellor of 1 * 40 * 2 * pi = 251 m/s, which is around 75% of the speed of sound. The tip acceleration would be 1*(40*2*PI)^2 = 63165 m/s^2 = 6445 g. 
If we are talking about fictional superheroes, they can accelerate and decelerate as fast as they like, because it is not real. The superhero would need some fairly impressive strength to accelerate at 6445 g though. If his mass was 50 kg, he would exert a force of 3.16 million Newtons (322275 kgf) when he jumped with this superhuman acceleration, which would make it likely he would damage the floor! 
A: If you consider a rotating propeller, it has the following properties:


*

*you can see that something is there

*you cannot see what it is; you just happen to know it

*you cannot count the blades or really distinguish the features at all

*you cannot even tell the distance to the blurry "thing" in front of you

*people are known to walk into running propellers because they are hard to see


This is especially true in the absence of specular reflections of bright sources of light.
Hence I would argue that it is possible for an object to move so quickly, in a confined space, without approaching the speed of light, that it has many characteristics of invisibility. If you exclude other indicators such as noise or wind, a human-sized object moving evenly enough within your confined space, with a typical low power diffuse room lighting, can be difficult to spot.
Whether this qualifies it to be called "invisible" is a matter of how you define the word. It's obviously impossible for the object to stop reflecting photons; it's all about human perception. If a human is looking at a moving superman, yet notices only the walls, then "invisible" seems a fair thing to call it, even if there was a blur that the observer failed to attribute correctly.
(and honestly, instead of arguing what "invisible" means to you or me, why don't we drop the contentious term and simply discuss the underlying concepts)
A: See http://en.wikipedia.org/wiki/Orders_of_magnitude_(time) and http://www.huffingtonpost.com/2012/12/30/why-do-we-blink-so-much-mental-rest_n_2377720.html
A blink lasts 0.1-0.4 seconds and we spend as much as 10% of our waking time with our eyes closed.   So a superhero with good timing can easily move without being seen.
A: I would think an object can be invisible to a human if it moves so fast that, within the time it passes the field of view of the human, it reflects too little light to be detected visually (human vision has very high, but still limited sensitivity to light). On the other hand, if the object moves so fast in air, it will produce a lot of noise and probably heat the air so much that the latter will be visible.
EDIT (08/22/2014): I would like to add that, theoretically, one can use metamaterial cloaking (http://en.wikipedia.org/wiki/Metamaterial_cloaking ) to be invisible. Whether such invisibility can be perfect, I don't know.
A: 
So here is the question, is it physically possible for a "human" (human size object) to move in a CONFINED environment (lets say, 20 m×20 m×10 m ) so fast that a regular person would be unable to SEE? If it is possible, how fast must this "person" be?

The human eye relies on reception of photons to "see" something. There is no speed below the speed of light where an object will not reflect or emit photons.  Speed has nothing to do with reflection and emission, except as you approach the speed of light, which is far above the speed a biological creature can attain under their own power.
So to answer your question technically, no, there is no speed where an object will cease to reflect or emit light in the conditions you've described.
However, you might consider perception as part of "seeing."  The human eye is analog, and the data is being processed by an analog brain.  The receptors measure the amount of light received and send signals - more if more light is present, fewer if less light is being received.
Further, being biological, there's an amount of delay involved.  You can turn on a light, and it won't be sensed instantly once photons start hitting the receptors, instead the receptors will ramp up their signal output, and when the light ceases, they will relatively slowly cease signalling to the brain.
It's this property that makes it appear that static images shown in a sequence of 25 frames per second or more are not indistinguishable as separate frames, but as video.  In essence, the receptors act as low pass filters.
So a sufficiently fast moving object might appear blurred to the human eye.
However, humans are able to perform Smooth Pursuit, where the eye can follow a target which will avoid the blur, and the consequences of Saccade don't cause the visible scene to disappear.
Smooth pursuit occurs up to 30 degrees per second, but this is a maximum in one direction.  The human eye moves more slowly when trying to go back and forth following an object in a small area of their visual range.
Paint a circle on a ceiling fan.  At the low and medium speeds you should be able to follow it with your eyes several feet away.  At high speed you should find that it starts to blur or lengthen, or that your eyes can't keep up and you start following it via saccade movements.
Now do the same thing with a desk fan - at most speeds you cannot follow it at all, and, in fact, the blades become transparent.  They aren't invisible, but the light reflecting off them provides the perception of invisibility, primarily because you can see objects behind them which should be obscured by them.
You can move your hands fast enough that your eyes cannot follow them using smooth pursuit, at arms length.  Focus on an object beyond your hands and as you move them quickly past your vision you will see just a blur.
At 20 meters from the target, there are humans capable of moving their hands quickly enough that you would see little more than a blur, and you would be able to see objects behind the area their hands are operating in.
However they would still be perceived, and you would know that their hands occupy that space.  So depending on what you mean by "see" the answer is either, "No, they will always be seen," or "Yes, it is possible to move a human hand fast enough within your field of view that you wouldn't perceive the hand, but only the blur, and it would never fully block your view to objects beyond it."
