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 \(\SI{4}{m/s^2}.\) As soon as the first car reaches a speed of \(\SI{6}{m/s},\) 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 \(\SI{6}{m/s},\) and accelerates at \(\SI{4}{m/s^2}\) until it reaches the speed \(\SI{20}{m/s}.\)

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

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