Torricelli's formula (kinematics)

This online calculator uses Torricelli's kinematic formula, which establishes a relationship between the final velocity of a body moving straight ahead with constant acceleration, its initial velocity, the amount of acceleration, and the distance traveled to find the unknown from the three known values.

The formula itself is: $v_{1}^{2}=v_{0}^{2}+2a\Delta s$

Torricelli's formula (kinematics)

Initial velocity, m/s

Final velocity, m/s

Acceleration, m/s²

Distance, m

Digits after the decimal point: 2

Torricelli's Formula.

Torricelli's formula is derived from the standard equations of kinematics for rectilinear motion with constant acceleration. The formula is convenient in that it does not require the use of time.

Here is how it is derived:
The formula that relates the final velocity to the initial velocity, time and acceleration:
$v_{1}=v_{0}+at$

The formula that relates the distance traveled to initial velocity, time, and acceleration:
$\Delta s=v_{0}t+a\frac {t^{2}}{2}$

From this formula, we express the square of time:
$t^{2}=2{{\frac {\Delta s-v_{0}t}{a}}}$

Then we square the first formula:
$v_{1}^{2}=v_{0}^{2}+2av_{0}t+a^{2}t^{2}$

Then we substitute the square of time:
$v_{1}^{2}=v_{0}^{2}+2av_{0}t+a^{2}\cdot2{\frac {\Delta s-v_{0}t}{a}}}$

Then we reduce the a and open the parentheses:
$v_{1}^{2}=v_{0}^{2}+2av_{0}t+2a\Delta s - 2a v_{0}t$

Once again we reduce and finally get the formula known as the torricelli's formula:
$v_{1}^{2}=v_{0}^{2}+2a\Delta s$

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PLANETCALC, Torricelli's formula (kinematics)