初定本
運動方程者，物理公式也，析物運動之狀。其系位移 s → {\displaystyle {\vec {s}}} 、始速度 u → {\displaystyle {\vec {u}}} 、終速度 v → {\displaystyle {\vec {v}}} 、加速度 a → {\displaystyle {\vec {a}}} 兼時間 t {\displaystyle t} 。
1. v = u + a t {\displaystyle v=u+at}
2. s = ( u + v ) t 2 {\displaystyle s={\frac {(u+v)t}{2}}}
3. s = u t + 1 2 a t 2 {\displaystyle s=ut+{\frac {1}{2}}at^{2}}
4. s = v t − 1 2 a t 2 {\displaystyle s=vt-{\frac {1}{2}}at^{2}}
5. v 2 = u 2 + 2 a s {\displaystyle v^{2}=u^{2}+2as}
一或書： v → = ∫ a → d t = u → + a → t {\displaystyle {\vec {v}}=\int {\vec {a}}dt={\vec {u}}+{\vec {a}}t}
三或書： s → = ∫ v → d t = ∫ ( u → + a → t ) d t = u → t + 1 2 a → t 2 {\displaystyle {\vec {s}}=\int {\vec {v}}dt=\int ({\vec {u}}+{\vec {a}}t)dt={\vec {u}}t+{\frac {1}{2}}{\vec {a}}t^{2}}
五或書： v → . v → = | v → | 2 = u → . u → + 2 a → . s → = | u → | 2 + 2 a → . s {\displaystyle {\vec {v}}.{\vec {v}}=|{\vec {v}}|^{2}={\vec {u}}.{\vec {u}}+2{\vec {a}}.{\vec {s}}=|{\vec {u}}|^{2}+2{\vec {a}}.{s}}
1. v → = ∫ a → d t = v 0 → + a → t {\displaystyle {\vec {v}}=\int {\vec {a}}dt={\vec {v_{0}}}+{\vec {a}}t}
2. s → = ∫ ( ∫ a → d t ) d t = ∫ v → d t = ∫ ( v 0 → + a → t ) d t = s 0 → + v 0 → t + a → t 2 {\displaystyle {\vec {s}}=\int (\int {\vec {a}}dt)dt=\int {\vec {v}}dt=\int ({\vec {v_{0}}}+{\vec {a}}t)dt={\vec {s_{0}}}+{\vec {v_{0}}}t+{\vec {a}}t^{2}}
3. | v → | 2 = | u → | 2 + 2 a → . s → {\displaystyle |{\vec {v}}|^{2}=|{\vec {u}}|^{2}+2{\vec {a}}.{\vec {s}}}
