The definition of average velocity is:

According to this definition, the vector average velocity is obtained by dividing a vector by a scalar.� Since the scalar () is always positive, this definition indicates that the two vectors (�and ) have the same direction.� We would like to apply this definition to find the velocity at the turning point.� Then �and �in the definition correspond to an interval that spans the turning point, i.e., with an initial point just before the turning point and with a final point just after the turning point.� The diagrams below illustrate this idea graphically for a ball that is turning around.

Suppose a ball rolls uphill past point 1, turns around at point 2 and then rolls downhill past point 3.� Since the ball has turned around, points 1 and 3 correspond to the same location.� The position of the ball is a vector that points from the origin to the location of the ball.� The location of the origin in the diagram is arbitrary.� Its location will not affect the velocity we are trying to compute.� Since points 1 and 3 represent the same point, the position vectors at these two instants are also the same.� If this is true, what is ?� What is ?

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