$8.(30$ pts$)$ Two cars, a red one and a blue one, start from rest and race down a flat level road for a distance of $2000$ m$.$ The blue cars driver has the fastest reaction time and when the starting flag drops. The red car accelerates with ar$=8\mathrm{.}0$ m$/$s$2$until reaching the red cars top speed vr$=90$ m$/$s$.$ The blue car can accelerate at only ab$=6\mathrm{.}5$ m$/$s$2$but has a top speed of vb$=110$ m$/$s$.$ The red cars driver misses the starting flag drop and starts the race tlag$=1\mathrm{.}5$ s later than the blue car.a$.$ Which car wins the race?b$.$ How much more time does the loser take to finish the race than the winner? In short the blue car starts first immediately at time t$=0$ and the red car lags behind starting $1\mathrm{.}5$ s later.