  For ASEP with step initial data and a second class particle started at the
origin we prove that as time goes to infinity the second class particle almost
surely achieves a velocity that is uniformly distributed on $[-1,1]$. This
positively resolves Conjecture 1.9 and 1.10 of [Amir, Angel and Valko, "The
TASEP speed process", Annals of Probability 39, 1205--1242, 2011] and allows us
to construct the ASEP speed process.
