# 數學模型

## 物理學

${\displaystyle \mathbf {F_{net}} =m\mathbf {a} }$ ；「一件物件受嘅淨力${\displaystyle \mathbf {F_{net}} }$ ）等如佢嘅質量${\displaystyle m}$ ）乘以加速度${\displaystyle \mathbf {a} }$ ）」，呢條定律又可以寫做
${\displaystyle \mathbf {F_{net}} ={\frac {d{\vec {p}}}{dt}}=m{\vec {a}}}$ ${\displaystyle p}$  係指動量（momentum；嚿物體嘅質量同速度相乘），而 ${\displaystyle {\frac {d{\vec {p}}}{dt}}}$  係動量隨住時間改變嘅率。
• 由古典力學嘅推論嗰度仲可以帶出動能（kinetic energy，KE）嘅概念，一件物件帶嘅動能可以用以下呢條式表達：
${\displaystyle \mathbf {KE} ={{1 \over 2}mv^{2}}}$ ，當中 ${\displaystyle v}$  係件物件嘅速度。

## 化學

• 考慮一場噉嘅化學反應
${\displaystyle {\ce {{{\mathit {a}}A}+{{\mathit {b}}B}->{{\mathit {p}}P}+{{\mathit {q}}Q}}}}$
• 當中 ${\displaystyle {\ce {A}}}$ ${\displaystyle {\ce {B}}}$ 反應物（做反應嘅原料），${\displaystyle {\ce {P}}}$ ${\displaystyle {\ce {Q}}}$  反應產物（場反應產生嘅物質），${\displaystyle {\ce {\mathit {a}}}}$ ${\displaystyle {\ce {\mathit {b}}}}$ ${\displaystyle {\ce {\mathit {p}}}}$ ${\displaystyle {\ce {\mathit {q}}}}$  反映化學計量數（簡化噉講即係「每 ${\displaystyle {\ce {\mathit {a}}}}$ ${\displaystyle {\ce {A}}}$  同每 ${\displaystyle {\ce {\mathit {b}}}}$ ${\displaystyle {\ce {B}}}$  會做反應出 ${\displaystyle {\ce {\mathit {p}}}}$  咁多粒 ${\displaystyle {\ce {P}}}$ ${\displaystyle {\ce {\mathit {q}}}}$  咁多粒 ${\displaystyle {\ce {Q}}}$ 」）[3]
• 假設場反應喺一個容量固定嘅封閉系統裏面發生，化學反應率（${\displaystyle v}$ ）嘅定義可以係：
${\displaystyle v=-{\frac {1}{a}}{\frac {d[\mathrm {A} ]}{dt}}=-{\frac {1}{b}}{\frac {d[\mathrm {B} ]}{dt}}={\frac {1}{p}}{\frac {d[\mathrm {P} ]}{dt}}={\frac {1}{q}}{\frac {d[\mathrm {Q} ]}{dt}}}$
－即係話一場化學反應嘅反應率可以由「啲反應物同反應產物嘅濃度${\displaystyle {\ce {A}}}$ ）隨時間嘅導數${\displaystyle {\frac {d[\mathrm {A} ]}{dt}}}$ ；簡單講即係濃度隨時間變嘅率）」嚟反映。

## 攷

1. Morin, David (2008). Introduction to Classical Mechanics. New York: Cambridge University Press. ISBN 9780521876223.
2. Barut, Asim O. (1980) [1964]. Introduction to Classical Mechanics. New York: Dover Publications. ISBN 9780486640389.
3. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006-) "Rate of reaction".