  We theoretically investigate the time-dependent ballistic transport in
metallic graphene nanoribbons after the sudden switch-on of a bias voltage $V$.
The ribbon is divided in three different regions, namely two semi-infinite
graphenic leads and a central part of length $L$, across which the bias drops
linearly and where the current is calculated. We show that during the early
transient time the system behaves like a graphene bulk under the influence of a
uniform electric field $E=V/L$. In the undoped system the current does not grow
linearly in time but remarkably reaches a temporary plateau with dc
conductivity $\sigma_{1}=\pi e^{2}/2h$, which coincides with the minimal
conductivity of two-dimensional graphene. After a time of order $L/v_{F}$
($v_{F}$ being the Fermi velocity) the current departs from the first plateau
and saturates at its final steady state value with conductivity
$\sigma_{2}=2e^{2}/h$ typical of metallic nanoribbons of finite width.
