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 2. The direction of the velocity at point D is 4. The diagram at right illustrates both of these vectors. The diagram also illustrates that the acceleration vector can be broken into two components: one component that is parallel to the velocity () and one component perpendicular to the velocity ().

describes how the magnitude of the velocity is changing. If points in the same direction as , then the object is speeding up. If the directions of and are opposite, then the object is slowing down. If is zero, then the object neither speeds up nor slows down.

describes how the direction of the velocity is changing. If is on the clockwise side of , then the object is turning clockwise. If is on the counterclockwise side of , then the object is turning counterclockwise. If is zero, then the object is moving in a straight line.

Is this true?

Is this true?