00:01
So a quick review of motion and motion graphs and how they relate to some calculus.
00:10
So recall that x will use x for position of an object.
00:20
And things are pretty boring unless the position changes.
00:24
So there are two different types of velocity.
00:28
One is called average, and it goes with delta x over delta t.
00:35
So delta x is called the displacement, which means that the position has to change, whereas instantaneous velocity is the derivative of x with respect to time.
00:56
But in any event, what both of these means is that velocity is the slope or measures how position changes.
01:10
In time.
01:19
And we could say that mathematically, it is the slope of position versus time.
01:40
Okay, so we can come up with an example.
01:44
Let's make a particle drawn x -axis.
01:51
And let's have the particle start at one and move to 2 over 3 seconds.
02:05
Okay, so 3 seconds.
02:08
Let's just move smoothly to 2.
02:13
And then let's say it sits there for 2 seconds.
02:23
And then let's let it go to minus 2 over the next, i don't know, 5 seconds.
02:38
What would that look like on both a position time and a velocity time graph? on a position time, it would be pretty simple.
02:51
It would move from one to two over three seconds.
03:05
It would sit there for two seconds.
03:09
Oh, sit there.
03:12
And then it would move backwards...