Solve Problem at Traffic Intersection: Can You Make It Through?

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To determine if a car can make it through three traffic lights without stopping, calculations show that a car traveling at 50 km/h will take approximately 6 seconds to reach the third light, which is within the 13 seconds the lights remain green. The first car can successfully pass all three lights without stopping. In contrast, the second car, which starts from a stop and accelerates at 2.0 m/s², will take longer to reach the speed limit and will not make it through all three lights without stopping. The distances between the lights are 55m and 85m, which factor into the timing for both vehicles. Overall, the first car can proceed uninterrupted, while the second car cannot.
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Each intersection has a traffic signal and the speed limit it 50km/h. Suppose you are driving from west at speed limit. When you are 10m from the first intersection all lights turn green. The lights are green for 13 seconds each. (a) calculate time needed to reach third stop light. Can you make it through all three lights without stopping? (b) Another car was stopped at first light when all the lights turned green. It can accelerate at the rate of 2.0m/s^2 to the speed limit. Can the second car make it through all three lights without stopping? From first light to the second light the distance is 55m. from the second light to third light distance is 85m.

Any help is greatly appreciated!
 
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