Question

diferences between root mean square speed and mean speed

Answer 1

The following information will possibly help you:
http://en.wikipedia.org/wiki/Root-mean-square_speed

Answer 2

rms is often used to give a magnitude for a varying parameter.

IF for instance you look at a sine wave - it is equal above and below the 'zero' line and hence its mean value is 0

However it has a magnitude (+ or -) and hence if you 'square' the value it becomes positive for all values. The root of this 'squared value' retains the same dimensions as the original measure and is a good indication of the 'magnitude' of the signal regardless of its sign.

This gives further examples of the use of this measure:
http://en.wikipedia.org/wiki/Root_mean_square