Why is the root mean square here calculated like this?

I can show you how the formula is generated:

https://www.electronics-tutorials.ws/accircuits/rms-voltage.html

Sine waves are still sines waves, no matter what's making them.

V = 1mm/s
f = 250 Hz
X = ?

1 mm/s = 2 * pi * 250 Hz * X
10^(-3) [m] / (2 * pi * 250) = X
1 / (500 * 1000 * pi) [m] = X
(1/(5 * pi)) * 10^(-5) meters = X
‭0.06366197723675813430755350534901‬... * 10^(-5) meters = X
6.3661977236.... * 10^(-2) * 10^(-5) meters
6.3661977236 * 10^(-7) meters

To 2 sf, that's 6.4 * 10^(-7) meters

Peak RMS involves the value of sin(45 degrees) or sqrt(2)/2 , or 0.707

((1/(5 * pi)) * 10^(-5)) / (sqrt(2)/2) =>
(sqrt(2)/(5 * pi)) * 10^(-5) =>
sqrt(2) * 6.4 * 10^(-7) =>
1.414 * 6.4 * 10^(-7) =>
‭9.0031631615710606955519919100674‬....

9 * 10^(-7) m