\(t^*:=(L/c)-(c/a)(\sqrt{1+((a/c)\, t^*)^2}-1),\)

\((a/c)\, T_{ABA}:=2\, \text{ArcSinh}[\, (a/c)\, t^*\, ].\)

\(t_m-t_i:=(c/b)(\sqrt{1+((b/c)\, t_m)^2}-1)+(L/c)-(c/a)(\sqrt{1+((a/c)\, t_i)^2}-1),\)

\(t_f-t_m:=(c/b)(\sqrt{1+((b/c)\, t_m)^2}-1)+(L/c)-(c/a)(\sqrt{1+((a/c)\, t_f)^2}-1).\)

\((a/c)\, t_f:=\text{Sinh}[\, \text{ArcSinh}[\, (a/c)\, t_i\, ]+(a/c)\, T_{ABA}\, ]\)

\(\implies (b/a)=\frac{1}{(a/c^2)\, L}=\text{Exp}[\, -(a/c)\, T_{ABA}\, ].\)

#ProofInAToot ? #ClaimInAToot #Acceleration