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Torricelli's equation
Encyclopedia
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:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-1.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-2.gif)
Square both sides to get:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-3.gif)
The term
appears in the equation for displacement, and can be isolated:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-5.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-6.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-7.gif)
Substituting this back into our original equation yields:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-8.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-9.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-10.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-11.gif)
Evangelista Torricelli
Evangelista Torricelli was an Italian physicist and mathematician, best known for his invention of the barometer.-Biography:Evangelista Torricelli was born in Faenza, part of the Papal States...
to find the final velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
of an object moving with a constant acceleration without having a known time interval.
The equation itself is:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-1.gif)
Derivation
Begin with the equation for velocity:![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-2.gif)
Square both sides to get:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-3.gif)
The term
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-4.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-5.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-6.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-7.gif)
Substituting this back into our original equation yields:
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-8.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-9.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-10.gif)
![](http://image.absoluteastronomy.com/images/formulas/2/2/2223760-11.gif)