transportation

Space Time Speed Pace and Mean

Legend: x-axis coordinate, x; length interval, Δx; unit of length, x̂; t-axis coordinate, t; time interval, Δt; unit of time, t̂. For scalars: Rates Speed/Pace Symbols Space Time Ordinary Time speed Δx(t)/t̂ measure length/distance/ displacement given period/unit Alternate Space speed x̂/Δt(x) given length/distance/unit measure interval/period /dischronment Inverse Space pace Δt(x)/x̂ given length/distance/unit measure interval/period /dischronment …

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Instantaneous time and space speed

This post relates to the previous one here. Speed is the time rate of distance traversed. Pace is the space rate of elapsed time. The time speed of a body is the distance traversed per unit of independent time without regard to direction, Δx/t̂. The instantaneous speed is the time speed at a point in …

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With and between independent variables

This post continues the previous post here on independent and dependent variables. The selection of a physical independent variable (or variables) applies to a context such as an experiment. Within that context all other variables are, at least potentially, dependent on the independent variable(s) selected. Functions with the physical independent variable as a functional independent …

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Distance as an independent variable

A previous post here gives “Motion as a Function of Distance” in which distance is a functional but not a physical independent variable. So distance is an independent variable of the inverse of the function of motion as a function of time. But this functional independence does not change the original independent variable of time. In …

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Independent and dependent variables

There are two kinds of independent variables: (1) functional independent variables, and (2) physical independent variables. To avoid confusion an independent variable it is standard that a variable be of both kinds, since being of one kind does not imply being of the other kind. A physical independent in an experiment remains the independent variable …

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Temporo-spatial rest

Speed is the length of travel per unit of duration (or time interval). Spatial rest is a speed of zero. That is, there is no change in location per unit of time. A body does not change location (relative to an inertial observer) while time continues. But temporal rest seems different. It cannot be zero …

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Space and time as frames

An observer is a body capable of use as a measurement apparatus. An inertial observer is an observer in inertial motion, i.e., one that is not accelerated with respect to an inertial system. An observer here shall mean an inertial observer. An observer makes measurements relative to a frame of reference. A frame of reference …

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Proper and improper rates

The independent quantity in a proper rate is the denominator. The independent quantity in an improper rate is the numerator. If a rate is multiplied by a quantity with the units of the independent quantity and the result has the units of the dependent quantity, it is proper. Otherwise, it is improper. A proper rate …

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Interchanging space and time

The space-time exchange invariance, as stated by J. H. Field (see here) has an implicit second part. In addition to (1) the exchange (or interchange) of space and time coordinates, there is (2): the exchange of series and parallel or harmonic algebra for ratios. This is seen in the different averaging methods for velocities that differ …

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