Torricelli's equation

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In physics, Torricelli's equation, or Torricelli's formula, is an equation created by Evangelista Torricelli to find the final velocity of a moving object with constant acceleration along an axis (for example, the x axis) without having a known time interval.

The equation itself is:^[1]

${\displaystyle v_{f}^{2}=v_{i}^{2}+2a\Delta x\,}$

where

• ${\displaystyle v_{f}}$ is the object's final velocity along the x axis on which the acceleration is constant.
• ${\displaystyle v_{i}}$ is the object's initial velocity along the x axis.
• ${\displaystyle a}$ is the object's acceleration along the x axis, which is given as a constant.
• ${\displaystyle \Delta x\,}$ is the object's change in position along the x axis, also called displacement.

In this and all subsequent equations in this article, the subscript ${\displaystyle x}$ (as in ${\displaystyle {v_{f}}_{x}}$) is implied, but is not expressed explicitly for clarity in presenting the equations.

This equation is valid along any axis on which the acceleration is constant.