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
Mass driver velocity would rather be around 62.75% of total mission delta v if operating at constant specific impulse, except greater optimization could come from varying exhaust velocity during the mission profile (as possible with some thruster types, including mass drivers and variable specific impulse magnetoplasma rockets). Since a mass driver could use any type of mass for reaction mass to move the spacecraft, a mass driver or some variation seems ideal for deep-space vehicles that scavenge reaction mass from found resources. One possible drawback of the mass driver is that it has the potential to send solid reaction mass travelling at