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. 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 along a straight and level track from point 1 to 2 to 3. Assume that the ball rolls at constant speed. Hence the lengths of the velocity arrows are all the same.

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

.

Since, the ball is rolling with constant velocity, and are equal. Hence, equals zero. In addition, the definition of acceleration implies that the acceleration must be zero as well.

In summary, the acceleration will be zero whenever an object moves with constant speed in a straight line.