- Torricelli's equation
Torricelli's equation is an equation created by
Evangelista Torricelli to find the finalvelocity 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 Delta d ,
Derivation
Begin with the equation for velocity:
v_f = v_i + at,!
Square both sides to get:
v_f^2 = (v_i + at)^2 = v_i^2 + 2av_it + a^2t^2,!
The term t^2,! appears in the equation for displacement, and can be isolated:
d = d_i + v_it + afrac{t^2}2
d - d_i - v_it = afrac{t^2}2
t^2 = 2frac{d-d_i - v_it}{a} = 2frac{Delta d - v_it}{a}
Substituting this back into our original equation yields:
v_f^2 = v_i^2 + 2av_it + a^2left(2frac{Delta d - v_it}{a} ight)
v_f^2 = v_i^2 + 2av_it + 2a(Delta d - v_it)
v_f^2 = v_i^2 + 2av_it + 2aDelta d - 2av_it,!
v_f^2 = v_i^2 + 2aDelta d,!
ee also
Equation of motion External links
* [http://demonstrations.wolfram.com/TorricellisTheorem/ Torricelli's Theorem] by Ernest Lee,
The Wolfram Demonstrations Project .
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