  We present a new approach to study (1+1)-dimensional Dirac equation in the
background of an effective mass $M$ by exploiting the possibility of a
position-dependent fermi velocity $v_f$. We explore the resulting structure of
the coupled equations and arrive at an interesting constraint of $M$ turning
out to be the inverse square of $v_f$. We address several solutions of the
effective potential that include the free particle, shifted harmonic
oscillator, Morse potential, and CPRS potential.
