The light will be red-shifted.
Work Step by Step
By the principle of equivalence, the accelerating railroad car is equivalent to a stationary one, standing vertically with its front end up. The light traveling from the back to the front of the accelerating railroad car is just like light traveling upward, climbing the gravitational field of a planet and losing energy. The energy of a photon is given by E = hf, where h is Planck's constant. If the energy of light is lowered, as in traveling upward in a gravitational field, its frequency is lowered (the light is said to be red-shifted).