  The kinetic uncertainty relation (KUR) is a trade-off relation between the
precision of an observable and the mean dynamical activity in a fixed time
interval for a time-homogeneous and continuous-time Markov chain. In this
letter, we derive the KUR on the first passage time for the time-integrated
current from the information inequality at stopping times. The relation shows
that the precision of the first passage time is bounded from above by the mean
number of jumps up to that time. We apply our result to simple systems and
demonstrate that the activity constraint gives a tighter bound than the
thermodynamic uncertainty relation in the regime far from equilibrium.
