Abstarct: Resently the AdS/CFT correspondence has been generalized to the descxription of some non-relativistic strongly coupled systems.In this research utilized the string theory and AdS/CFT correspondence.Such computing , significantly help us to understanding the using vest implementation of AdS/CFT correspondence.For this purpose the open string in the non-relativistic background be considered. Dual of this problem,is the motion of particle with constant velocity in the non-relativistic vacuum space with zero temperature.The lost energyof particle is not zero.If a particle move in the relativistic vacuum space at zero temprature , do not force it.This important difference is an interesting result,which need to be realized for more studies. By concidering the equation of motion of a particle which moves in the along compact direction , we understand one of possible solutions , can be a string that in two ends of string are particle and antiparticle.Then the distance between them will be achived by using string theory.Also , the potential between particle and antiparticle , obtained and about convexity conditions will be discussed. For generalization to new cases , have been considered the motion of particle along non-compact direction and the equation of motion will be studied.It is demonstrated the non-relativistic space have effective influence on the motion of particle.