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Quantity Equation in Coherent Units
How should a physical quantity equation be expressed?
✍: FYIcenter.com
A physical quantity equation should be expressed
with quantities in coherent units to avoid conversion factors.
The following equation assumes that v, v and v are in SI coherent units:
where
v is the velocity in m/s
d is the distance in m
t is the time in s
The following equation has coherent units specified explicitly:
<math> <msub><mrow> <mo>{</mo> <mi>v</mi> <mo>}</mo>
</mrow> <mrow> <mi mathvariant="normal">m</mi>
<mo lspace="0" rspace="0">/</mo>
<mi mathvariant="normal">s</mi>
</mrow> </msub> <mo>=</mo>
<msub><mrow> <mo>{</mo> <mi>d</mi> <mo>}</mo>
</mrow> <mi mathvariant="normal">m</mi></msub>
<mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
<msub><mrow> <mo>{</mo> <mi>t</mi> <mo>}</mo>
</mrow> <mi mathvariant="normal">s</mi></msub> </math>
If we change the velocity unit to km/h, the same equation will have a conversion factor:
<math> <msub><mrow> <mo>{</mo> <mi>v</mi> <mo>}</mo>
</mrow> <mrow> <mi mathvariant="normal">km</mi>
<mo lspace="0" rspace="0">/</mo>
<mi mathvariant="normal">h</mi>
</mrow> </msub> <mo>=</mo> <mn>3.6</mn> <mo>×</mo>
<msub><mrow> <mo>{</mo> <mi>d</mi> <mo>}</mo>
</mrow> <mi mathvariant="normal">m</mi></msub>
<mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
<msub><mrow> <mo>{</mo> <mi>t</mi> <mo>}</mo>
</mrow> <mi mathvariant="normal">s</mi></msub> </math>
⇐ Quantity Expressed with Value and Unit
2026-10-28, ∼1937🔥, 0💬
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