It seems to me that "fast time" in model railroading exists because destinations are not prototypical distances from one another. That is, if two destinations were 48 miles apart (separated by 48 miles of track), then an O-scale model would have one mile of track between the two locations. Not many modelers have the luxury of accommodating that distance of track.
And IMO, time is not scaled. Dimensions and distance are scaled and time works itself out.
Of course I find the calculation done by the OP meaningless, but here goes...
The math for the example in the OP's post of the formula for an object dropped from earth is:
- s = 1/2g(t^2)
- where s is the distance the object travels, g is acceleration due to gravity, and t is time
If s = 480 ft, then 480 = 1/2 (32.2)(t^2)
or 480 = 16.1 (t^2)
or t^2 = 29.8 sec^2
or t = 5.46 sec
