One beam isn't enough. You should consider two (or maybe even more) light beams for the entrance and similarly for the exit.

What would happen if the car breaks just when the front bumper breaks the light, and then it rolls back an inch and then rolls forward again?

Real systems would probably use proximity sensors to pick up the magnetic field around the vehicles. And they would have some mechanism to only allow one car at a time to pass.

Having multiple light beams, you can implement something similar to an optical rotary detector counting pulses in forward/reverse direction of a shaft by keeping track of the phase of the two beams. A car hasn't passed unless it breaks both beams in the correct order and unblocks the two beams in the correct order.

But even with a multi-beam solution, you may get an error, requiring you to have a way to correct the count.

Just as with keyboard switches, you will need some form of debounce logic for each beam. If you need to modulate the ray or not will depend on how clever you are with debouncing and with processing the readings from multiple beams. But it would most probably be advantageous for you to use IR instead of visible light.