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Torricelli's Equation

From Biocrawler, the free encyclopedia.

This equation was created by Evangelista Torricelli to find the final velocity of a moving object without having a known time and was named after him.

The equation itself is:

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

This can be found from those two other formulas:

$d = d_i + v_i t + \frac {( a t^2 )} {2} \,$

and

$v_f = v_i + a t \,$

Isolating the time from the second equation, we have:

$v_f = v_i + a t \,$

$v_f - v_i = a t \,$

$t = \frac {( v_f - v_i )} {a} \,$

And now, substituting this equation on the first one, we get:

$d = d_i + v_i t + \frac {( a t^2 )} {2} \,$

$d - d_i = v_i \left (\frac {v_f - v_i} {a} \right) + \frac {a} {2} \left(\frac {v_f - v_i} {a} \right)^2 \,$

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

$\Delta d = \frac {v_f v_i - v_i^2} {a} + \frac {v_f^2 - 2 v_f v_i + v_i^2} {2a} \,$

$\frac {2a \Delta d} {2a} = \frac {2 v_f v_i - 2 v_i^2} {2a} + \frac {v_f^2 - 2 v_f v_i + v_i^2} {2a} \,$

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

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

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

[edit]

Torricelli's Equation

From Biocrawler, the free encyclopedia.

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