Proper Velocity

Proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object.

The proper velocity equals the velocity in the observer reference frame divided by the square root of 1 minus the square of the ratio of the velocity in the observer's reference frame and the speed of light.

Formula

QuantityVariable["W", "Speed"] == QuantityVariable["v", "Speed"]/Sqrt[1 + Quantity[-1, "SpeedOfLight"^(-2)]*QuantityVariable["v", "Speed"]^2]

symbol	description	physical quantity
W	proper velocity	"Speed"
v	velocity in observer reference frame	"Speed"

Forms

Examples

Open in Wolfram Cloud

Download Example Notebook

Get the resource:

In[1]:=

Out[1]=

Get the formula:

In[2]:=

Out[2]=

Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Proper Velocity"], {QuantityVariable["v","Speed"] -> Quantity[1.`*^8, ("Meters")/("Seconds")]}]$

Out[3]=

External Links

http://en.wikipedia.org/wiki/Proper_velocity

Publisher Information

Enable JavaScript to interact with content and submit forms on Wolfram websites. Learn how