why dont you simply tell me what you think the answers are
then see if I agree to them.

meanwhile , I have calculated the braking force of the single mass that is accelerated at 5 m/s/s for a distance
of 152.4 meters = 500 ft.

I get the following , you can check the math for yourself.

500 kg-m/s/s or 500N
100 kg mass
5m/s/s = 500N/100kg

initial velocity = 0m/s
final velocity = 39.0385 m/s
average velocity = 19.51925 m/s
distance the mass traveled in 7.8077 seconds = 152.400448225 meters

so the single mass is traveling into the turnaround at
a velocity of 39.0385 m/s
3903.85 N = 100 kg * 39.0385 m/s

the braking force required to stop the single mass is
3903.85 N

at any time durring acceleration the 20 masses being pushed by the 500 kg-m/s/s or 500N are pushing back on the pipe with the same force with a combined force of 500N * 20 = 10000N

we had used 500 kg as the mass of the pipe earlier in the discussion so the 10000N force applying to the 500kg mass
results in a acceleration of 20 m/s/s

20m/s/s = 10000N/500kg

so there is a constant force of 10000N applied to the pipe
at any moment durring acceleration of the 20 100 kg masses.

initial pipe velocity = 0m/s
initial mass velocity = 0m/s

given that all of the masses are distributed evenly
around in the system , by the time a single mass is accelerated between the first turnaround and the next turnaround
the pipe has a final velocity of 156.154 m/s
the pipes average velocity is 78.077 m/s

78077N = 500 kg * 156.145


78077 N - 3903.85 N = 74173.15 N

we can keep dilly dallying around with examples but using the pipe example would be best.

to an observer outside the pipe the pipe has moved 609.6017929 meters after 7.8077 seconds.

just in case you are curious in 1 hour , 3600 seconds
the pipe will have traveled 129,600,000 meters
or 80,529.706 miles

its final velocity will be 72000 m/s or 44 miles / second

or 2684.323 mph

in 24 hours it will travel 39,158,514.937 miles
or 74649600000 meters

in 1 week 3657830400000 meters or 1,918,767,231.937 miles

and that is by using only 1 set of masses , a space ship could be fitted with hundreds of these tubes and each extra tube adds that much more acceleration , I need to set the program to calculate the speed and time to the nearest star.

what would the fastest acceleration be that humans could withstand?

3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.