It's Green

The distance between any two adjacent cars at a red light is 2 meters.

As soon as the light turns green, the first car starts accelerating at 4 m/s2.\SI{4}{m/s^2}. As soon as the first car reaches a speed of 6 m/s,\SI{6}{m/s}, the second car starts accelerating at the same rate. In exactly the same fashion, each successive car starts accelerating when the car in front of it reaches 6 m/s,\SI{6}{m/s}, and accelerates at 4 m/s2\SI{4}{m/s^2} until it reaches the speed 20 m/s.\SI{20}{m/s}.

When all cars have reached the same speed 20 m/s,\SI{20}{m/s}, how far apart are two adjacent cars (in meters)?

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