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Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
Velocity refers to a displacement in one direction with respect to an interval of time. It is defined as the rate of change of displacement over change in time. [7] Velocity is a vector quantity, representing a direction and a magnitude of movement. The magnitude of a velocity is called speed.
From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, s. In calculus terms, the integral of the velocity function v(t) is the displacement function s(t). In the figure, this corresponds to the yellow area under the curve.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.) The same multiplication rule holds true ...
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
The relative velocity of an object B relative to an observer A, denoted (also or ), is the velocity vector of B measured in the rest frame of A. The relative speed v B ∣ A = ‖ v B ∣ A ‖ {\displaystyle v_{B\mid A}=\|\mathbf {v} _{B\mid A}\|} is the vector norm of the relative velocity.
The radial velocity or line-of-sight velocity of a target with respect to an observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative velocity onto the relative direction or line-of-sight (LOS) connecting the two points.