Is rms velocity not a vector quantity? (EK Physics #865)

[MediCynical]

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Background: The question is in relation to a parallel plate capacitor in which a positively charged particle moves back and forth with AC current, but never touches either plate. One complete cycle (back and forth) is done in T seconds.

If the object in apparatus A reaches a maximum velocity of 20 m/s, what is the rms velocity of the object in the first T seconds?

A) 0 m/s
B) 10 m/s
C) 14 m/s
D) 20 m/s

Answer: C

OK, I understand that the rms value of anything is just the amplitude divided by the square root of 2, but this question is asking about the velocity over a period of time, T, in which the particle changes directions and presumably reaches the same velocity in both directions... Shouldn't it be 0 m/s???

 

[fizzgig]

no i don't think so, because it involves squaring the velocity over timepoints.

that's exactly why AC electricity usage is based on RMS current drawn i think, because if they charged based on the current actually going through your system it'd be zero (the current is traveling in and out cyclically).

 

[lorenzomicron]

nope, root mean square velocity is a kind of "average velocity" of the wave, in this case 20/sqrt(2).

In other terms, let the velocity v= 20*sin(2*pi*f*t + phi).
it is true that the velocity is sometimes zero, but it is actually at least its rms value or above 50% of the time.

the rms value of the AC (oscillating) current is actually the average value of the AC current; if one had an AC source, then one could replace it with a DC source that had its value as the rms of the AC source.

and, in any case, rms is just a defined kind of quanity...