Question

A race car makes one lap around a track of radius 50 m in 9.0 s. What is the average velocity? *

Answer 1

With velocity, you have to be careful.  With velocity, it doesn't matter how much total distance you covered while you were moving.  All that matters is the straight-line distance between the place you started from and the place where you stopped.  

If you ended in the same place where you started from, then it doesn't matter whether you drove around town all day and then came home, or ran around laps on a circular track, or zig-zagged back and forth a hundred times.  The straight distance from your start-point to your end-point is zero.  So technically, according to the defintion of velocity, it was ZERO.