2012 Semifinal Exam Part B 14 v(0)=QA-aB=0 These equations have solution A=B=号 and therefore z0=号+2 c.This time our initial values are x(O)=A+B=0 v(0)=QA-aB=vo with solution A=8 B=8 Therefore 0=- 20 After a long time,the second (e-at)term will become negligible.Thus,the second particle will approach the first particle if the first term matches: oeat boeat 20 Uo =QT0 Copyright C2012 American Association of Physics Teachers2012 Semifinal Exam Part B 14 v(0) = αA − αB = 0 These equations have solution A = B = x0 2 and therefore x(t) = x0 2 e αt + x0 2 e −αt c. This time our initial values are x(0) = A + B = 0 v(0) = αA − αB = v0 with solution A = v0 2α B = − v0 2α Therefore x(t) = v0 2α e αt − x0 2α e −αt After a long time, the second (e −αt) term will become negligible. Thus, the second particle will approach the first particle if the first term matches: x0 2 e αt = v0 2α e αt v0 = αx0 Copyright c 2012 American Association of Physics Teachers