How does one moving slowly cause the others to go faster and faster?
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It’s just geometry. There’s probably a better explanation for this, but think of pizza sizes. You know instinctively that a 3 inch diameter pizza is tiny but a 6 inch diameter pizza is multiple times larger.
The same applies to gears. Gear chains are attached to their inner parts, so the energy to turn them 360 degrees is mostly the same whether they’re tiny or large. But the large ones are really huge and cover really large distances on every 360 revolution. The tiny ones cover almost no distance.
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