Wolfram Computation Meets Knowledge

Proper Velocity Using Rapidity

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 hyperbolic sine of the rapidity times the speed of light.

Formula

QuantityVariable["W", "Speed"] == Quantity[1, "SpeedOfLight"]*Sinh[QuantityVariable["θ", "Rapidity"]]

symbol description physical quantity
W proper velocity "Speed"
θ rapidity "Rapidity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Proper Velocity Using Rapidity"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Proper Velocity Using Rapidity"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[
 ResourceObject[
  "Proper Velocity Using Rapidity"], {QuantityVariable[
   "\[Theta]","Rapidity"] -> 0.6`}]
Out[3]=

Publisher Information