Work out root mean square speed instantly with clear inputs, formula shown and shareable results.
Kinetic theory gives the root mean square speed as sqrt(3RT/M). Nitrogen at 300 K averages 517 m/s - faster than a rifle bullet. The Maxwell-Boltzmann distribution also defines a mean speed of sqrt(8RT/piM) and a most probable speed of sqrt(2RT/M), which sit in the ratio 1.225 : 1.128 : 1.
RMS speed
v(rms) = sqrt(3 R T / M)
Distribution speeds
v(mean) = sqrt(8RT/piM); v(mp) = sqrt(2RT/M)
The Maxwell-Boltzmann distribution is skewed, so its peak, mean and root-mean-square all differ. RMS is the one tied to kinetic energy.
Because they collide constantly - billions of times a second - so the net progress is a slow random walk rather than a straight dash.