The definition of average acceleration is:

According to this definition, the vector average acceleration 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 direction of the acceleration at point D which is a turning point. Then and in the definition correspond to an interval that spans point D, i.e., an interval with an initial point just before point D and with a final point just after point D. The diagrams below illustrate this idea graphically.

Suppose that a ball rolls uphill along a straight track from point 1 to 2. Point 2 is a turning point. Afterward, the ball rolls back downhill from point 2 to 3. Points 1 and 3 are the same point. As the ball rolls uphill, it slows down. As it rolls downhill, it speeds up. .

Recall that the change in velocity between the final point (point 3) and the initial point (point 1) is:

.

This is equivalent to saying that is the quantity that must be added to the initial velocity in order to obtain the final velocity:

The diagram at right shows the vector (the red vector) that must be graphically added to vector to obtain . Hence, the red vector must be .

According to the definition of average acceleration,

Since is a positive scalar, the direction of the acceleration must be the same as the direction of the change in velocity. The relative magnitudes of the and depends on the value of .

If the interval is short enough, then the average acceleration for the interval is equal to the instantaneous acceleration at the midpoint of the interval, point 2. This is illustrated in the diagram at right. Notice that the acceleration points down the incline.

In summary, the acceleration at a turning point is not zero. It points down the incline.