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A two$-$way and two$-$lane roadway is heavily travelled by trucks and semi$-$trailers. Therefore, the design length of an overtaken vehicle is $22$ m$.$ The design speed of the roadway is $80$ km$/$h$.$ Determine the overtaking distance required for a car, if the design acceleration of the car $2$ m$/$s$2$ on a flat route with $0\%$ slope. The following distance before overtaking is given by the empirically stated equation of d$=0\mathrm{.}4$v where d is in meters and v is in km$/$h $($speed of the car that is followed$).$ The distance between the overtaking car and the overtaken vehicle is also d$=0\mathrm{.}4$v$.$ The speed of the car coming from the opposite direction is $80$ km$/$h$.$ The safety distance between the overtaking car and the car coming from the opposite direction after the completion of overtaking is $90$ m$.$ Draw a sketch and estimate the required overtaking distance.