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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Torricelli's equation ： ウィキペディア英語版 Torricelli's equation In physics, Torricelli's equation is an equation created by Evangelista Torricelli to find the final velocity of an object moving with a constant acceleration without having a known time interval. The equation itself is: :$v\_f^2\; =\; v\_i^2\; +\; 2\; a\; \backslash Delta\; d\; \backslash ,$ where *$v\_f$ is the object's final velocity *$v\_i$ is the object's initial velocity *$a$ is the object's acceleration *$\backslash Delta\; d\; \backslash ,$ is the object's change in position == Derivation == Begin with the equation for velocity: :$v\_f\; =\; v\_i\; +\; at\backslash ,\backslash !$ Square both sides to get: :$v\_f^2\; =\; (v\_i\; +\; at)^2\; =\; v\_i^2\; +\; 2av\_it\; +\; a^2t^2\backslash ,\backslash !$ The term $t^2\backslash ,\backslash !$ appears in the equation for displacement, and can be isolated: :$d\; =\; d\_i\; +\; v\_it\; +\; a\backslash frac2$ :$d\; -\; d\_i\; -\; v\_it\; =\; a\backslash frac2$ :$t^2\; =\; 2\backslash frac\; =\; 2\backslash frac$ Substituting this back into our original equation yields: :$v\_f^2\; =\; v\_i^2\; +\; 2av\_it\; +\; a^2\backslash left(2\backslash frac\backslash right)$ :$v\_f^2\; =\; v\_i^2\; +\; 2av\_it\; +\; 2a(\backslash Delta\; d\; -\; v\_it)$ :$v\_f^2\; =\; v\_i^2\; +\; 2av\_it\; +\; 2a\backslash Delta\; d\; -\; 2av\_it\backslash ,\backslash !$ :$v\_f^2\; =\; v\_i^2\; +\; 2a\backslash Delta\; d\backslash ,\backslash !$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Torricelli's equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.