A model known as stopping sight distances=2g(f±G)V2​VwhereSVgfGT= stopping sight distance (ft) 

is used by civil engineers to design roadways. This simple model estimates the distance a driver needs in order to stop his car while traveling at a certain speed after detecting a hazard. The model proposed by the American Association of State Highway Officials (AASHO) is given by

$\genfrac{}{}{0ex}{}{{}^{}}{}+T$

$\begin{array}{rl}& \\ & =\text{ initial speed (ft/s) }\\ & \\ & \\ & ={\text{ acceleration due to gravity, 32.2 ft/s }}^2\\ & =\text{ coefficient of friction between tires }\\ & \text{ and roadways }\\ & =\text{ grade of road }\\ & =\text{ driver reaction time (s) }\end{array}$

What are the appropriate units for f and G if the preceding equation is to be homogeneous in units? Show all steps of your work.