One driver is driving on a $3\%$ upgrade roadway with an initial speed of $80$ mph $,$ assuming his

perception$-$reaction time is $2$ seconds, do the following:

a$.$ If the driver has to slow down to $0$ mph to completely stop in front of an intersection.

A stop warning sign for the intersection is clearly visible for a distance of $100$ ft $.$ How far

in advance of the intersection must the sign be posted in order to insure that vehicles

can safely stop, using deceleration rate $=9f\frac{t}{se{c}^2}?$

b$.$ Redo part a with the default deceleration rate.

c$.$ Redo part a$,$ assuming deceleration rate is unknown but the friction factor$=0\mathrm{.}2.$