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https://en.formulasearchengine.com/w/index.php?title=Latin_letters_used_in_mathematics&diff=9740
Latin letters used in mathematics
2013-12-07T02:02:40Z
<p>128.84.124.136: added "the principal quantum number" as one of the uses of n</p>
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<div>{{distinguish|Torricelli's law|Torricelli's theorem|Torricelli's trumpet|Torricelli point}}<br />
{{Unreferenced|date=January 2008}}<br />
<br />
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.<br />
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The equation itself is:<br />
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:<math> v_f^2 = v_i^2 + 2 a \Delta d \,</math><br />
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== Derivation ==<br />
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Begin with the equation for velocity:<br />
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:<math>v_f = v_i + at\,\!</math><br />
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Square both sides to get:<br />
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:<math>v_f^2 = (v_i + at)^2 = v_i^2 + 2av_it + a^2t^2\,\!</math><br />
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The term <math>t^2\,\!</math> appears in the equation for displacement, and can be isolated:<br />
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:<math>d = d_i + v_it + a\frac{t^2}2</math><br />
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:<math>d - d_i - v_it = a\frac{t^2}2</math><br />
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:<math>t^2 = 2\frac{d-d_i - v_it}{a} = 2\frac{\Delta d - v_it}{a}</math><br />
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Substituting this back into our original equation yields:<br />
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:<math>v_f^2 = v_i^2 + 2av_it + a^2\left(2\frac{\Delta d - v_it}{a}\right)</math><br />
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:<math>v_f^2 = v_i^2 + 2av_it + 2a(\Delta d - v_it)</math><br />
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:<math>v_f^2 = v_i^2 + 2av_it + 2a\Delta d - 2av_it\,\!</math><br />
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:<math>v_f^2 = v_i^2 + 2a\Delta d\,\!</math><br />
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==See also==<br />
* [[Equation of motion]]<br />
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== External links ==<br />
* [http://encyclopedia2.thefreedictionary.com/Torricelli%27s+equation Torricelli's theorem]<br />
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{{DEFAULTSORT:Torricelli's Equation}}<br />
[[Category:Kinematics]]</div>
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