Convert mile / square second to foot / (minute • second)
Learn how to convert
1
mile / square second to
foot / (minute • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{minute \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mile}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{foot}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{0.3048}{60.0}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{0.3048}{60.0}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{minute \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{0.3048}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{0.3048}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{0.3048}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(1609.344 = {\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{60.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{60.0} = 1609.344\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{60.0}{0.3048}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{60.0} \times \dfrac{60.0}{0.3048} = 1609.344 \times \dfrac{60.0}{0.3048}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{0.3048}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{0.3048}}} = 1609.344 \times \dfrac{60.0}{0.3048}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 60.0}{0.3048}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 316800 = 3.168 \times 10^{5}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mile}{square \text{ } second}\right) = {\color{rgb(20,165,174)} 3.168 \times 10^{5}}\left(\dfrac{foot}{minute \times second}\right)\)
