加速度

概要

${\displaystyle {\Delta }=t'-t}${\displaystyle {\Delta }=t'-t}

${\displaystyle {\Delta v}={\boldsymbol {v}}(t')-{\boldsymbol {v}}(t)}${\displaystyle {\Delta v}={\boldsymbol {v}}(t')-{\boldsymbol {v}}(t)}

${\displaystyle {\boldsymbol {a}}=\lim _{\Delta t\to 0}{\Delta {\boldsymbol {v}} \over \Delta t}\equiv {\frac {d{\boldsymbol {v}}}{dt}}}${\displaystyle {\boldsymbol {a}}=\lim _{\Delta t\to 0}{\Delta {\boldsymbol {v}} \over \Delta t}\equiv {\frac {d{\boldsymbol {v}}}{dt}}}

${\displaystyle a_{r}={\frac {d^{2}r}{dt^{2}}}-r\!\left({\frac {d\theta }{dt}}\right)^{2}}${\displaystyle a_{r}={\frac {d^{2}r}{dt^{2}}}-r\!\left({\frac {d\theta }{dt}}\right)^{2}}

${\displaystyle a_{\theta }={\frac {1}{r}}{\frac {d}{dt}}\!\left(r^{2}{\frac {d\theta }{dt}}\right)}${\displaystyle a_{\theta }={\frac {1}{r}}{\frac {d}{dt}}\!\left(r^{2}{\frac {d\theta }{dt}}\right)}

等加速度運動

${\displaystyle a(t)={\boldsymbol {a_{0}}}}${\displaystyle a(t)={\boldsymbol {a_{0}}}}

${\displaystyle t=0}${\displaystyle t=0}

${\displaystyle {\boldsymbol {v(t)}}=v_{0}+a_{0}t}${\displaystyle {\boldsymbol {v(t)}}=v_{0}+a_{0}t}

${\displaystyle {\boldsymbol {x(t)}}=x_{0}+v_{0}t+{\frac {1}{2}}a_{0}t^{2}}${\displaystyle {\boldsymbol {x(t)}}=x_{0}+v_{0}t+{\frac {1}{2}}a_{0}t^{2}}

${\displaystyle {\boldsymbol {v(t)^{2}}}-{\boldsymbol {v_{0}^{2}}}=2a_{0}x(t)}${\displaystyle {\boldsymbol {v(t)^{2}}}-{\boldsymbol {v_{0}^{2}}}=2a_{0}x(t)}

単位

脚注

注釈

1. ^ 物体の速度の、各時間の点での変化の割合。

出典

1. ^ ^{a b} 小出昭一郎 1997, p. 8.
2. ^ 世界大百科事典内の等加速度運動の言及
3. ^ 時間 t を含まない式

参考文献

関連項目

外部リンク