Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
Secondary ion mass spectrometry the SIMS type, there are three basic analyzers available: sector, quadrupole, and time-of-flight. A sector field mass spectrometer uses a combination of an electrostatic analyzer and a magnetic analyzer to separate the secondary ions by their mass-to-charge ratio. A quadrupole mass analyzer separates the masses by resonant electric fields, which allow only the selected masses to pass through. The time of flight mass analyzer separates the ions in a field-free drift path according to their velocity. Since all ions possess the same kinetic energy the velocity and therefore time of flight varies according to mass. It requires pulsed secondary ion