00:01
Okay, so basically the displacement in meters of particle moving in a straight line is given by s is equal to t squared and then showed a question mark in the actual like, you know, question that you submitted.
00:13
But i'm going to assume that it's a negative.
00:15
So i've seen similar questions as this before.
00:19
So basically it's s is equal to t squared minus six.
00:25
Let me just fix the t actually, minus 6t plus 18.
00:33
This is really important.
00:35
So, s is equal to t squared minus 6t plus 18.
00:43
And first it wants you to find the average velocity over different intervals.
00:46
So the first one's going to be three to four.
00:51
Now, for this one, basically finding the average interval means that you find the average velocity for each interval.
01:02
So basically the average velocity is going to be the change in s over the change.
01:06
Change in t.
01:08
So it's basically just going to mean, so i'm going to put average.
01:15
Velocity is equal to the change in s over the change in d.
01:21
So basically we want to find what s is at three and four and then divide that by the change in t.
01:30
T or this are just these two numbers right over here.
01:33
The numbers you plug into t right over here.
01:35
And the change in t is going to be four minus three basically.
01:38
It's literally the t.
01:41
Minus the other t.
01:44
So first let's plug it in and see what we get for three and four.
01:47
And we're going to basically just divide that by the change in t.
01:54
So first we're going to do s3 and then s4.
02:01
Now we can calculate that.
02:02
So three squared.
02:04
So it's going to be, i was right like this, three squared minus six times three plus 18.
02:12
So it's going to be nine.
02:14
Minus 18 plus 18.
02:16
Well, that's just 9.
02:17
So i'm going to say 9.
02:20
And then four, it's going to be four squared minus six times four plus 18.
02:28
And that's going to be, um, it's going to be 16 minus 24 plus 18.
02:38
Let me sure i did my math right.
02:40
And, uh, it's going to be minus six.
02:43
It's going to be 10 right over here, i believe.
02:45
Let me just double check that to make sure my math isn't being messed up.
02:49
Sometimes i make really dumb mistakes when it comes to this.
02:52
But it looks like i was right, it is plus 10.
02:58
And now we're going to do the change in s over the change in t.
03:02
So it's going to be 10 minus 9 over 4 minus 3.
03:08
Well, that's as 1 over 1.
03:09
So the answer is a 1.
03:13
And it's going to be 1 meter per second because it's meters at the top over time which is second so meters per second.
03:28
Two is going to be 3 .5 and 4.
03:40
So first we're going to do s3 .5 and then s4.
03:44
S4 we already calculated.
03:45
This is going to be 10.
03:46
So we save a little bit of time there.
03:48
But 3 .5 we got to solve.
03:50
So we're going to do 3 .5 squared.
03:54
Minus six times 3 .5 plus 18.
04:03
And that should give us, i'm going to use my calculator because i can't really do 3 .5 times 3 .5 in my head.
04:11
That will.
04:12
It's going to be 12 .25.
04:14
So it's going to be 12 .25 minus.
04:17
And it's going to be 6 times 3 .5.
04:24
It's going to be minus 21 plus...