00:01
In this video, i'm going to be looking at two of our kinematics equations and showing you the derivation of them.
00:08
So our first equation is final velocity squared equals initial velocity squared plus two times acceleration times distance traveled.
00:20
And my second equation is final position equals initial position plus initial velocity times time.
00:32
Plus one half acceleration times time squared.
00:38
All right.
00:39
So we want to derive these two equations.
00:41
I'll start with number one.
00:44
And i'm going to use two other equations we have.
00:48
I know my acceleration equals my change in velocity over change in time.
00:56
That equals v final minus v initial over time.
01:02
Time.
01:03
For this video, i'm assuming initial time will always be zero so we can get rid of that t initial factor.
01:11
I also have a definition for position where i have d equals initial velocity plus final velocity over two times time.
01:27
And again, for this video, my initial position at t equals zero is also zero.
01:32
So we don't need to worry about that d initial term.
01:35
Right, and we can multiply these two equations times each other.
01:39
I'll get a times d.
01:42
That equals v final minus v initial over t times v final, or sorry, v initial plus v final over two times t.
01:58
And i'll rewrite this on the next page and we can simplify it...