Atire of radius r rolls in a straight line without slipping. its center moves with constant speed v. a small pebble lodged in the tread of the tire touches the road at t = 0. find the pebble’s position, velocity, and acceleration as functions of time.

i've seen solutions before, starting with breaking the motion into x and y coordinates, like so

v(x)=v-rw*cos(wt)

v(y)=v(1-cos(wt))

i do not conceptually understand how these equations are derived, use pictures if nessecary.