Does the acceleration vector always point in the direction in which an object is moving? If not, describe a situation as an example.

No, acceleration does not always point in the direction in which the object is moving.

The vector that indicates the direction of motion is the velocity vector. The velocity vector is always tangent to the trajectory (path) of the object, and it indicates the direction in which the object moves at a given moment.

The acceleration, by definition, is the change of the velocity vector in a small amount of time. So if the velocity...

No, acceleration does not always point in the direction in which the object is moving.

The vector that indicates the direction of motion is the velocity vector. The velocity vector is always tangent to the trajectory (path) of the object, and it indicates the direction in which the object moves at a given moment.

The acceleration, by definition, is the change of the velocity vector in a small amount of time. So if the velocity is changing, it indicates the direction in which the velocity is changing.

For example, consider a train that is slowing down. The velocity vector of the train points in the same direction, but its magnitude becomes smaller. This means the change of the velocity vector, `Delta vecv` , is pointing opposite the velocity vector, and thus opposite the direction of the motion of the train. The acceleration vector points in the same direction as `Delta vecv` , opposite to the motion of the train.

Another example is seen with circular motion. Consider a child on a merry-go-round moving in a circle with constant speed. The acceleration of the child points towards the center of the circle, normal (perpendicular) to the child's trajectory. The velocity of the child is tangent to the circle. Here, the acceleration of the child is perpendicular to the direction of his motion, indicated by the velocity vector.