Çözüldü Kinematics - Application of Integral

A solved example from the University of Saskatchewan:


https://i72.servimg.com/u/f72/19/97/10/39/kinema10.png
https://math.usask.ca/~au/MATH110F20/MATH110_23.pdf
(Pages 12 - 13, Example 3)

Alternate Solution for a Test Exam: 40^2 / (2·10) = 80 meters.

Note:
Using equations about distance (S), velocity (initial: v0 and final: v), time (t), and acceleration (a),
S = v0·t + (1 / 2)(-a)·t^2....(I)
v = v0 + (-a)·t....(II)
From the equation (II), t = (v0 - v) / a....(III)
Substituting (III) in (I), S = v0·[ (v0 - v) / a ] - (1 / 2)·a·[ (v0 - v) / a ]^2
S = (2·v0^2 - 2v·v0 - v0^2 + 2v·v0 - v^2) / (2a)
S = (v0^2 - v^2) / (2a)....(IV)
Taking v = 0 in (IV), S = v0^2 / (2a).