CyberSurfer, when dealing with moving objects, the direction as well as the speed is important. Going 100 miles per hour south is not the same as going 100 miles per hour west. The concept of speed combined with direction is called velocity. Velocity can be represented as a line with an arrow at one end: -------> . The direction of the line indicates the direction of the motion, while the length corresponds to the speed. The line is called a velocity vector. A lot of problems involving velocity can be visualized and solved by applying geometric methods to the vectors (lines).

Does the above help you understand what a vector is?

Kedaman, I did not understand your equations.

Angle from center between points: a=2pi/pradius (I think this should be a = 2*pi/P for radians, or 360/P for degrees), but since you do not use it anywhere, I guess it does not matter.

r=50/sin((1/8-1/(2*P))*PI)
I just do not understand this equation nor the next. Why not r = 50/sin(a/2)?
Speed vector component to centre: v=500*cos(1/4-1/p)*pi (Why not 500*cos(a/2)?)

At any rate, for the square, the distance traveled has to be 100 miles. I remember this from the formal solution using differential equations. At 500 mph, the time has got to be 12 minutes. Your formulae do not seem to give this result, nor do my variations on your formulae.