To determine how far we travel in that time, it will be helpful to get everything into feet per second rather than miles per hour.

Input := 

fspeed[r_] = 5280 30(1-1/(r+1)^(1/4))/3600;

Our top speed in feet per second is

Input := 

MaxLineFPS = Limit[fspeed[r], r -> Infinity]

Output =

44

Our maximum deceleration in feet per second squared is the same as the maximum acceleration:

Input := 

MaxDecFPS2 = 5280 2/3600 

Output =

44
--
15

Input := 

MaxAccFPS2 = MaxDecFPS2;

And our speed along the quarter circle must be

Input := 

MaxTurnFPS = fspeed[30] //N

Output =

25.3529