Difference between Trajectory and Displacement

Trajectory

For kinematics, the trajectory of a body is the locus of the positions it passes through as it moves. It depends on a reference system in which said movement is described, that is, the point of view of the observer.

For classical mechanics, the trajectory of a body is always a continuous line, while for quantum mechanics there are situations that are not. For example, the position of an electron in an atom’s orbital is probabilistic.

Displacement

The displacement is the vector that defines the position of a point or particle in relation to a point of origin with respect to a position. The vector extends from a reference point to the final position. In the displacement only the initial position and the final position matter and its trajectory does not matter.

For dynamics, the displacement is the vector or straight segment that joins the initial position with another generic point of the trajectory. This vector fully describes the motion and path of a particle during its trajectory.

Differences between trajectory and displacement

• Displacement is a vector that indicates distance and direction traveled by an object.
• The trajectory is a locus that indicates the positions of a particle or object during its motion.
• The offset has a reference point that can be found at the initial position of the object.
• The trajectory has a reference point located at the observer’s position.