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I know the mathematical definition of the RMS velocity. What I'm looking for is the logical...

I know the mathematical definition of the RMS velocity. What I'm looking for is the logical definition. Example: The average velocity of a group of cars can be related to a balancing point for the group. What would the RMS velocity be considered/related to in this example?

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suppose there are 10 cars, 5 of which are travelling towards right and 5 towards left, all with same velocity, V. Now since velocity is a vector quantity we have to allot signs. Lets say right as positive, then naturally, left will be negative. so then 5 cars have velocity V and the other 5 have -V. We end up with average velocity as zero. To eliminate this problem we make use of rms velocity which is "the square root of the average of squares of the velocities". Squaring up makes the negative signs to disappear and hence we do not end up with the default result as zero.

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