Stopping (or any other) path from the given initial conditions
Given
Initial position, velocity and acceleration
Path

where
(0)
with:
(1)

(2)

(3)
assuming

and

(3)
we get:
(4)
(5)
assuming (positive alpha velocity):
(6)
and from(5)
(7)
derivating further:
(8)
(9)
multiplying above (9) by n:
(10)
and from (9):

(11)