Convert gravity to mile / square minute
Learn how to convert
1
gravity to
mile / square minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gravity\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(gravity\right) = {\color{rgb(89,182,91)} 9.80665\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 9.80665\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mile}{square \text{ } minute}\right) = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gravity\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.80665} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(9.80665 = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times 10^{3}} = 9.80665\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{1609.344}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{1609.344} = 9.80665 \times \dfrac{3.6 \times 10^{3}}{1609.344}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1609.344}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{1609.344}}} = 9.80665 \times \dfrac{3.6 \times 10^{3}}{1609.344}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.80665 \times 3.6 \times 10^{3}}{1609.344}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx21.936851288\approx21.9369\)
\(\text{Conversion Equation}\)
\(1.0\left(gravity\right)\approx{\color{rgb(20,165,174)} 21.9369}\left(\dfrac{mile}{square \text{ } minute}\right)\)
