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.

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction 

Did you ever figure out the right answers since you asked?

A=v^2/r solve for r hope that  

Cannot be determined because i dont  know this but i need the points