and how fast is the top of the tyre (tire) travelling?
The bottom of the tire is travelling at the same speed as the ground itself. (This must be so, else the tire would skid against the ground.) That means that, relative to an observer sitting on the curb, the speed of the bottom of the tire is zero (same as the ground). But relative to the CYCLIST, the speed of the bottom of the tire is 10 mph toward the rear (again, same as the ground). Now, regarding the top of the tire: First look at it from the point of view of the cyclist. Since (as we established before) the tire's bottom is travelling 10mph rearward, the tire's top must be travelling 10mph forward. Again, this is relative to the cyclist. Now look at it from the point of view of the observer on the curb. The cyclist is travelling 10mph forward relative to the observer; and the tire's top is traveling 10mph forward relative to the cyclist. So the tire's top relative to the observer is going 10mph forward + 10mph forward 20mph forward.
That depends on the size of the wheel and what gear you are in. However, in one sense it is progressing at the same rate as the rest of the bike.
Velocity of bottom is ZERO, and velocity of the top is twice the speed of the bike 2x10mph 20mph. Momentarily axis of rotation of the wheel is loctated where the tire touches the ground.
