 Passage through a translating optical trap

For a force profile supported on an interval of width $w$, set $u=F/\zeta$. If a trap of speed $v$ overtakes an overdamped particle with $v-u>0$, then $\Delta t=\int dy/(v-u)$ and $\Delta x=v\Delta t-w$. These expressions follow by changing to the trap-frame coordinate, whose velocity is $u-v$. Smooth zeroes of $v-u$ can prevent finite passage.