Dynamics and radiation of a charged particle moving in a constant electromagnetic field and possessing a linear dispersion law ε(p) = νF|p| are considered. This dispersion law is typical for electrons in graphene and similar nanostructures. A general solution to the equation of particle motion is found. Explicit expressions for emitted energy are derived. It is shown that for |Hz| ≤ vF|Ex|, the energy emitted by the electron during infinite time period remains finite.