The problem with your situation is that you’re assuming the segments should all be the same length. Instead, the segments should be designed that the walker spends the same amount of TIME on each segment. So as you go to faster and faster ones, they’d have to get progressively longer.
For example, let’s assume they are all 10 ft. When he’s walking 2mph, he’d go 10 feet in about 3.4 seconds. When he’s walking on the ramp going 2mph, he’d go 10 feet in 1.7 seconds. When he’s on the next ramp, he’d go 10 feet in 1.13 seconds. At this point he’s only going 6mph, but already the ramps are so short that he probably doesn’t have enough time to take a step before he hits the next ramp. Pretty soon he’s going to hit a ramp and just fall.
So let’s assume that the belts are designed with increasing lengths so that he always spends 2 seconds on each.
The speed he would be moving in mph would be equal (2 + t), where t is the number of seconds that has been walking - after 2 seconds, he’d be at (2+2) = 4mph; after 60 seconds, he’d be at (60+2)=62mph.
However, the length of each belt would be:
length = 2.933 * (t)
So the “60mph belt” would have to be 176 feet long. The total length required to get up to 60mph would be 2728 feet, or nearly half a mile. Assuming the same amount of length to decelerate, you would take about 2 minutes to cover a mile, or averaging about 30mph.
If you wanted to get up to 120mph, the individual track section would be twice as long (352 ft), but total length would be four times as much (10736 ft).
But one big problem is, no matter how slowly you accelerate, the “seam” between sections is still stationary. So if you’re moving at 60mph, that gap between belts will approach you at 60mph. You’d have to have really quick reflexes to be able to step over it. Just imagine being on an escalator at the mall, and having it moving at 60mph. Ignoring the quick deceleration when you step off, you still will have a lot of trouble stepping off at just the right time.