▁The ▁relativ istic ▁momentum ▁relation ▁takes ▁the ▁same ▁form ▁as ▁for ▁classical ▁momentum , ▁but ▁using ▁the ▁above ▁relativ istic ▁mass : ▁▁ ▁Rel ativ istic ▁kin etic ▁energy : ▁The ▁relativ istic ▁kin etic ▁energy ▁relation ▁takes ▁the ▁slightly ▁modified ▁form : ▁. ▁ ▁N umer ical ▁values ▁▁ ▁In ▁the ▁table ▁below , ▁the ▁left - hand ▁column ▁shows ▁spe eds ▁as ▁different ▁fra ctions ▁of ▁the ▁speed ▁of ▁light ▁( i . e . ▁in ▁units ▁of ▁c ). ▁The ▁middle ▁column ▁shows ▁the ▁corresponding ▁Lor ent z ▁factor , ▁the ▁final ▁is ▁the ▁reci pro cal . ▁Val ues ▁in ▁bold ▁are ▁exact . ▁ ▁Altern ative ▁representations ▁ ▁There ▁are ▁other ▁ways ▁to ▁write ▁the ▁factor . ▁A bove , ▁velocity ▁v ▁was ▁used , ▁but ▁related ▁variables ▁such ▁as ▁momentum ▁and ▁rapid ity ▁may ▁also ▁be ▁convenient . ▁ ▁M oment um ▁Sol ving ▁the ▁previous ▁relativ istic ▁momentum ▁equation ▁for ▁ ▁leads ▁to ▁. ▁This ▁form ▁is ▁rarely ▁used , ▁although ▁it ▁does ▁appear ▁in ▁the ▁Max well – J ütt ner ▁distribution . ▁ ▁Rap id ity ▁App lying ▁the ▁definition ▁of ▁rapid ity ▁as ▁the ▁hyper bol ic ▁angle ▁: ▁ ▁also ▁leads ▁to ▁ ▁( by ▁use ▁of ▁hyper bol ic ▁ident ities ): ▁ ▁Using ▁the ▁property ▁of ▁Lor ent z ▁transformation , ▁it ▁can ▁be ▁shown ▁that ▁rapid ity ▁is ▁add itive , ▁a ▁useful ▁property ▁that ▁velocity ▁does ▁not ▁have . ▁Thus ▁the ▁rapid ity ▁parameter ▁forms ▁a ▁one -