Posted by **stranger** on Monday, May 27, 2013 at 9:07am.

Consider a horizontal road with such a set of traffic lights, each spaced 100 m apart. A car sits at the first traffic light. At t=0 the light turns green and the car accelerates. What is the maximum time t in secondsthe next light must turn green by so the driver of the car does not start braking?

Details and assumptions

The car has a total mass of 1000 kg and the acceleration of gravity is−9.8 m/s2.There is no delay between when a light changes color and the driver starts to accelerate/brake (ignore human reaction time).The car accelerates/brakes at 4 m/s2.The driver tries to go as fast as possible, while staying at or below the speed limit of 60 km/hr.If the driver sees a red light, they will brake (at 4 m/s2) such that they stop directly under the light.

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