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Instantaneous velocity of a falling object that has travelled distance on a planet with mass , with the combined radius of the planet and altitude of the falling object being , this equation is used for larger radii where is smaller than standard at the surface of Earth, but assumes a small distance of fall, so the change in is small and ...
The comoving distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula (derived using the Friedmann–Lemaître–Robertson–Walker metric): = ′ (′) where a(t′) is the scale factor, t e is the time of emission of the photons detected by the observer, t is the present time, and c is the speed of ...
Equation [3] involves the average velocity v + v 0 / 2 . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows ...
In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement , distance , velocity , acceleration , speed , and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time.
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 = = =.
Affine motion estimation is a technique used in computer vision and image processing to estimate the motion between two images or frames. It assumes that the motion can be modeled as an affine transformation (translation + rotation + zooming), which is a linear transformation followed by a translation.
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.)
Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation: