Torricelli's equation

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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 \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 + a\frac{t^2}2

d - d_i - v_it = a\frac{t^2}2

t^2 = 2\frac{d-d_i - v_it}{a} = 2\frac{\Delta d - v_it}{a}

Substituting this back into our original equation yields:

v_f^2 = v_i^2 + 2av_it + a^2\left(2\frac{\Delta d - v_it}{a}\right)

v_f^2 = v_i^2 + 2av_it + 2a(\Delta d - v_it)

v_f^2 = v_i^2 + 2av_it + 2a\Delta d - 2av_it\,\!


v_f^2 = v_i^2 + 2a\Delta d\,\!

See also

Equation of motion

External links

Wikipedia content modification information:

  • This page was last modified on 19 October 2008, at 04:01.

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