This means that Vmax is reached after 12.64mm travel distance and 0.19s time. During the 0.19s the stepper must receive 5056 pulses,
The above bit is correct, the 280kHz is not correct.
if the stepper steps 5056 steps in 0.19 seconds, then in 1 second, it will step 5056/0.19 = 26,610 steps / sec (or pulses / sec .... i.e. equivalent to 26,610 hz or ~ 26.6kHz)
not sure how you got 280 khz mathematically.
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Given we know that the whole acceleration cycle takes 0.19 seconds from zero to 8000mm/min = 133mm/s (Vmax)
Or to put it another way to go from zero to 53.2kHz
The time between the first & 2nd pulse will be 2.672mSec (equivalent to a 374 hz pulse trane time).
The velocity at the end of the first pulse will be 1.87mm/sec,
then the 3rd step comes in and the pulse time will be shorter as the equivelent pulse trane time increases all the way up to an equivalent 53.2khz.