Convert foot / second to inch / second
Learn how to convert
1
foot / second to
inch / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{foot}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{foot}{second}\right) = {\color{rgb(89,182,91)} 3.048 \times 10^{-1}\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} 3.048 \times 10^{-1}\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{second}\right) = {\color{rgb(125,164,120)} 2.54 \times 10^{-2}\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} 2.54 \times 10^{-2}\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{foot}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 3.048 \times 10^{-1}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.54 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 3.048 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.54 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 3.048 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.54 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(3.048 \times 10^{-1} = {\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(3.048 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}} = {\color{rgb(20,165,174)} x} \times 2.54 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-2}}}\)
\(\text{Simplify}\)
\(3.048 = {\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-1}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-1} = 3.048\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.54 \times 10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-1} \times \dfrac{1.0}{2.54 \times 10^{-1}} = 3.048 \times \dfrac{1.0}{2.54 \times 10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}} = 3.048 \times \dfrac{1.0}{2.54 \times 10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.048}{2.54 \times 10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 3.048}{2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 12\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{foot}{second}\right) = {\color{rgb(20,165,174)} 12}\left(\dfrac{inch}{second}\right)\)
