The measurement that relates to the distance something has moved is?

Displacement is the correct choice because it specifically refers to the change in position of an object and considers the straight-line distance from the initial position to the final position, along with the direction. In physics and engineering, displacement is a vector quantity, meaning it has both magnitude and direction. This is particularly important in vibration analysis, where understanding how far a component has moved from its equilibrium position can be crucial in diagnosing issues related to vibration and mechanical performance.

Although distance is a measure of how much ground an object has covered during its motion, it does not account for the direction and is a scalar quantity. Velocity and acceleration are also related to motion but describe rates of change rather than the actual movement itself, with velocity indicating how fast an object is moving and in which direction, and acceleration measuring how quickly the velocity changes over time. Thus, displacement accurately captures the essence of the movement discussed in the question.