Average acceleration is defined as:

.

Notice that in this definition, one vector is equal to another divided by a scalar. Since the scalar () is always positive, the two vectors ( and ) must have the same direction. Hence, the direction of the average acceleration is the same as the direction of the change in velocity. Remember that a velocity can change in two different ways:

1. The magnitude of the velocity can change (i.e., the object can speed up or slow down).

2. The direction of the velocity can change (i.e., the object can turn).

You indicated that the direction of the acceleration at point D is into the page. The direction of the velocity at point D is 4. The acceleration vector can be broken into two components: one component that is parallel to the velocity () and one component perpendicular to the velocity (). Since the velocity is in the plane of the track and your acceleration is perpendicular to the track, is zero and is directed into the page.

describes how the magnitude of the velocity is changing. Since is zero, the object neither speeds up nor slows down.

describes the direction in which the velocity is turning. The velocity will turn toward the direction of .

for the acceleration you selected is zero. This indicates that when the object is at point D, it is neither speeding nor slowing down. Is this true?

for the acceleration you selected indicates that the velocity is turning into the page. Is this true?