(Solved): Car A is traveling at a location where the speed limit is 100km/h. The police officer in car P o ...

Car $$A$$ is traveling at a location where the speed limit is $$100\mathrm{km}/\mathrm{h}$$. The police officer in car $$P$$ observes this speed via radar. The driver of car $$A$$ is traveling at $$v_A=126\mathrm{km}/\mathrm{h}$$ as it passes $$P$$, but over the next 5.9 seconds, the car uniformly decelerates to the speed limit of $$100\mathrm{km}/\mathrm{h}$$, and after that the speed limit is maintained. At the moment when $$A$$ passes $$P$$, the police car begins to accelerate at the constant rate of $$5.3\mathrm{m}/{\mathrm{s}}^2$$ until a speed of $$155\mathrm{km}/\mathrm{h}$$ is achieved, and that speed is then maintained. Determine the distance s required for the police officer to overtake car $$A$$.