Velocity - Revision history

Lfox: Created page with "The '''velocity''' of an object is the rate at which it moves. A particle is an entity considered as a point. == Specification == There is no such thing as the velocity of a particle at "an instant in time." But I want to specify a certain ''real'' measurement, which could actually be done, and which is the reality-based analogue of that notion. If one measures a particle and it is not moving (relative to me), then he can measure it at a certain position $x$
2024-04-23T00:09:14Z

Created page with "The '''velocity''' of an object is the rate at which it moves. A particle is an entity considered as a point. == Specification == There is no such thing as the velocity of a particle at "an instant in time." But I want to specify a certain ''real'' measurement, which could actually be done, and which is the reality-based analogue of that notion. If one measures a particle and it is not moving (relative to me), then he can measure it at a certain position <math>x</m..."

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The '''velocity''' of an object is the rate at which it moves.

A particle is an entity considered as a point.

== Specification ==
There is no such thing as the velocity of a particle at "an instant in time." But I want to specify a certain ''real'' measurement, which could actually be done, and which is the reality-based analogue of that notion.

If one measures a particle and it is not moving (relative to me), then he can measure it at a certain position <math>x</math>, at a certain time <math>t</math>. Like all measurements, these come with uncertainties, <math> u_x^0 </math> and <math>u_t^0</math>, based on the nature of one's measurement apparatuses. If a particle is moving, then its measurement becomes more uncertain; one has less of an idea of what its position is at a given time. Denote the uncertainty of the moving particle by <math>u_x</math>. Then

'''Specification.''' The velocity of the particle at time <math>t</math> is <math display="block">v_t := \frac{u_x - u_x^0}{u_t^0}</math>I can get something like a fundamental theorem of calculus out of this, but it's very subtle because it depends on the exact specifications of the uncertainties.