Q:

What happens if you ride a bike on to a moving sidewalk?

If a person were to riding a bicycle on normal ground then ride onto a conveyer moving in the forward direction of the bicycle (like a moving sidewalk in an airport), would the bike slow down or speed up?

A:

Relative to a stationary observer, you and the bike would speed up once going on the conveyor belt. Essentially, biking on a convey belt merely adds to your velocity relative to that stationary observer.
However, a distinction should be made that the conveyor belt is supplying kinetic energy to you and your bike; you aren't yourself supplying more energy to move the bike to speed it up.

