Final answer:
The direction of the acceleration vector is indeed dependent upon the direction of motion and whether an object is speeding up or slowing down, making the statement true. Acceleration involves changes in speed or direction or both, with acceleration in the same direction as motion causing speeding up and in the opposite direction causing slowing down.
Step-by-step explanation:
The direction of the acceleration vector is indeed dependent upon both the direction the object is moving and whether the object is speeding up or slowing down. This statement is true. An object is considered to be accelerating if there is any change in its velocity, which can occur as a change in speed or a change in direction, or both. When the object's acceleration is in the same direction as its motion, the object is speeding up. Conversely, when an object's acceleration is in the opposite direction of its motion, the object is slowing down. Speeding up and slowing down are not to be confused with positive and negative acceleration.
For example, if a car is moving forward (positive velocity) and the acceleration vector is also forward (positive acceleration), the car is speeding up. However, if the car continues to move forward but the acceleration vector is backward (negative acceleration), then the car is slowing down. Lastly, if a car turns a corner at a constant speed, it is also accelerating because its direction is changing, indicating that acceleration is not just about the speed, but also the direction of motion.