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# The $x$-components of velocity of some particles (in $km/s$) are $6,4,2,0,-2,-4,-6$. The root-mean-square (rms) velocity calculated from these data (in $km/s$) is nearest to?

(A) 0 (B) 2 (C) 4 (D) 6

$v_{rms}$ (root mean square velocity) $= \Large \sqrt {\frac{ \sum_{n}^{i=1} v_i^2}{n}}$, where n is the number of particles.
Given our data, $v_{rms} = \large \sqrt{ \frac{6^2+4^2+2^2+0+(-2)^2 + (-4)^2 + (-6)^2}{7}}$
$\Rightarrow v_{rms} = 4$
edited Aug 9, 2014