  We prove global Lipschitz stability for inverse source and coefficient
problems for first-order linear hyperbolic equations, the coefficients of which
depend on both space and time. We use a global Carleman estimate, and a crucial
point, introduced in this paper, is the choice of the length of integral curves
of a vector field generated by the principal part of the hyperbolic operator to
construct a weight function for the Carleman estimate. These integral curves
correspond to the characteristic curves in some cases.
