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Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement.
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 = = =.
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.)
Stated formally, in general, an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = dr / dt ), and its acceleration (the second derivative of r, a = d 2 r / dt 2 ), and time t. Euclidean vectors in 3D are denoted throughout in bold.
Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.)
On the top is the time-position diagram. Objects representing tautochrone curve A tautochrone curve or isochrone curve (from Ancient Greek ταὐτό ( tauto- ) 'same' ἴσος ( isos- ) 'equal' and χρόνος ( chronos ) 'time') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest ...
Discrete integral calculus is the ... gives the distance (time ... or second difference quotient of the spatial position. Starting from knowing how an object is ...
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.