  We consider a run an tumble particle with two velocity states $\pm v_0$, in
an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae
for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic
$f(x)$ of period $L$. They involve the "active potential" which allows to
define a global bias. Upon varying parameters, such as an external force $F$,
the dynamics undergoes transitions from non-ergodic trapped states, to various
moving states, some with non analyticities in the $V_L$ versus $F$ curve. A
random landscape in the presence of a bias leads, for large $L$, to anomalous
diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we
calculate.
