Displacement (vector)
A displacement is the shortest distance from the initial and final positions of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A displacement vector represents the length and direction of that imaginary straight path.
A position vector expresses the position at a point in space in terms of displacement from an arbitrary reference point (typically the origin of a coordinate system). Namely, it indicates both the distance and direction of an imaginary motion along a straight line from the reference position to the position of the point. Thus, a displacement may be also described as a relative position: the final position of a point relative to its initial position, and a displacement vector can be mathematically defined as the difference between the final and initial position vectors.
In considering motions of objects over time the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The velocity then is distinct from the instantaneous speed which is the time rate of change of the distance traveled along a specific path.
If a fixed origin is defined we may then equivalently define the velocity as the time rate of change of the position vector. However if one considers a time dependent choice of origin as in a moving coordinate system the rate of change of the position vector only defines a relative velocity.
For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity.
In dealing with the motion of a rigid body, the term displacement may also include the rotations of the body. In this case, the displacement of a particle of the body is called linear displacement (displacement along a line), while the rotation is called angular displacement.
See also
- Position vector
- Affine space
References
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