A TRACK HAS A RADIUS OF 20 METERS...

Find circumference.

circumference=2pradius=125.7m

How many meters along the track corresponds to one radian?
 
1rad          * 125.7meters      =20meters
2prad

NOTE: This should be a common sense answer because the definition of one radian is "the angle subtended when radius equals arc length."

If you go around the track 5.5 times, how many meters have you gone?  How many radians?
 
 
125.7meters * 5.5laps =691m
        lap

 
2prad *5.5laps =34.6rad
lap
or if you like the exact math answer, 11p
If you start out from rest and accelerate at .5r/s/s for 10 seconds, how far will you have gone?

q=at²/2 = (.5r/s/s)(10s)²/2 = 25rad,    or in meters, 25rad*20m/rad=500m

How far would you go (in meters, radians, and laps) if you moved at 10m/s for 100sec?

d=s*t = 10m/s*100sec = 1000m

now we can either switch directly to radians (or we could convert m/s to rad/s and do the problem again, but I wont here)
1000m*1rad/20m = 50 rad

then divide by 2pi to get laps...

50rad* 1 lap/2p = 8 laps

Login to Lecture OnLine an in the 1D Motion Chapter, solve "Circle Displacement".