Question

The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 20 mph requires 28 ft to stop, find the stopping distance for a car traveling at 65 mph

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\

s= {\color{red}{ n}}v^2\qquad v=20mph\qquad s=28ft\implies 28= {\color{red}{ n}}(20)^2\)

solve for"n" to find the "constant of variation"

once you find "n", plug it back in the original equation

to "find the stopping distance for a car traveling at 65 mph" just set v = 65 for the original equation