Chapter P.3, Problem 82E

Stopping distance, The stopping distance of an automobile is the distance travelled during the driver’s reaction time plus the distance travelled after the driver applies the brakes. In an experiment, researchers measured these distances (in feet) when the automobile was traveling at a speed of $x$. miles per hour on dry, level pavement, as shown in the bar graph. The distance travelled during the reaction time $R$ was

$R=1.1x$

and the braking distance $B$ was

$B=0.0475x^2-0.001x+\mathrm{0.23.}$

(a) Determine the polynomial that represents the total stopping distance $T.$

(b) Use the result of part (a) to estimate the total stopping distance when $x=30,x=40,$ and $x=55$ miles per hour.

(c) Use the bar graph to make a statement about the total stopping distance required forincreasing speeds.