No, the acceleration vector is not always aligned with the velocity vector. The acceleration vector represents the rate of change of velocity with respect to time, but its direction and magnitude can be independent of the velocity vector.
In general, the acceleration vector has two components: magnitude and direction. The magnitude of acceleration determines how quickly the velocity is changing, while the direction of acceleration indicates the direction in which the velocity is changing.
There are three possible scenarios regarding the alignment of the acceleration vector with the velocity vector:
Acceleration and velocity are parallel: When the acceleration vector is parallel to the velocity vector, it means that the magnitude of velocity is increasing or decreasing. In this case, the object is either speeding up or slowing down, but it is not changing its direction. The acceleration can be in the same direction as velocity, indicating positive acceleration, or in the opposite direction, indicating negative acceleration (deceleration).
Acceleration and velocity are perpendicular: When the acceleration vector is perpendicular to the velocity vector, it means that the object is changing its direction but not its speed. This situation occurs in circular motion or when an object is subjected to a centripetal force. The object's velocity vector is constantly changing its direction, while the speed remains constant.
Acceleration and velocity have arbitrary angles: In many cases, the acceleration vector can have an arbitrary angle with respect to the velocity vector. This situation indicates that the object is simultaneously changing its speed and direction. The magnitude and direction of acceleration determine the specific changes in speed and direction.
Therefore, while the acceleration vector can be aligned with the velocity vector in certain cases, such as when the object is only changing its speed, it is not always the case. The direction of the acceleration vector depends on the specific circumstances and forces acting on the object.