We know that the lift formula is:
$Y= Cy0.5 ρv^2s$
We all know that.
$F = ma$ (1)
Let the aircraft take off with uniform acceleration, zero initial speed, $a$ acceleration, $v$ final speed and $x$ distance
According to the formula of uniformly accelerated motion,
$a = 0.5v ^ 2/x$ (2)
Substitute Formula (2) into Formula (1) and get
$F = 0.5 mv ^ 2/x$ (3)
Multiplication of formula (3) with $s/s$ is obtained.
$F = 0.5mv ^ 2s/xs$ (4)
xs is volume, so formula (4) is
$F = 0.5 ρv ^ 2s $ (5)
Since the wing has an angle of attack, it is necessary to modify the (5) mode.
$F=Cy0.5 ρv^2s$ (6)
And formula (6) is the lift formula.