设加速度为a,经过OA的时间为t1,经过AB和BC的时间为t2,OA的长度为x
则x=OA=1/2at1^2,L1=AB=1/2a(t+t1)^2-1/2at1^2=1/2at^2+att1
L2=BC=1/2a(2t+t1)^2-1/2a(t+t1)^2=3/2at^2+att1
L2-L1=at^2,L2/L1=(3/2t+t1)/(1/2t+t1)
∴a=(L2-L1)/t^2,t1=t/2*(3L1-L2)/(L2-L1)
∴x=OA=1/2at1^2=1/2*(L2-L1)/t^2*[t/2*(3L1-L2)/(L2-L1)]^2
=1/8*(L2-L1)/t^2*t^2*(3L1-L2)^2/(L2-L1)^2
=1/8*(3L1-L2)^2/(L2-L1)