00:01
All right, we've got a red train and a green train.
00:03
So i'll write this in red and green.
00:07
Velocity is going to be 72 kilometers per hour, but there's a thousand kilometers in a meter.
00:22
No, there's 1 ,000 meters in a kilometer.
00:30
And there's 3 ,600 seconds in an hour.
00:35
Meters per second.
00:38
And the green train, oh my goodness, is going twice that speed.
00:43
I'll just write to vr.
00:52
Initially, the distance apart is 950 meters.
01:00
The deceleration is 1 meter, per second squared? is there a collision? so, for the red drain, x equals v times t minus, no, no, plus, because i wrote a minus down here, one half a t squared.
01:49
But, okay, but also v final, which is going to be zero equals vr minus at.
02:19
I mean plus at because i have a minus down here already.
02:23
Okay, so that would be for the red train.
02:26
Now, for the green train, xg is going to be vg, which is 2vr.
02:44
Times t sub g uh so i need a sub r on these um plus one half a times uh t g squared and um the second equation 0 equals v, sorry, 2vr plus a, tg.
03:21
Okay, so solving for t subg, i get t subg is negative 2vr over a.
03:43
Solving up here, t subr is going to be negative vr over a.
03:51
So now i can substitute into both equations.
03:56
X subr is going to be v subr times t subr.
04:03
T subr is negative v sub r over a, plus one half a v sub r over a, squared.
04:16
X sub g is going to be 2 v sub r times negative 2 v sub r over a plus one half a 2vr over a squared.
04:46
Okay.
04:48
So so just simplifying here, that's going to be v.
04:53
R squared over a, negative v.
04:56
R squared over a, plus one -half v.
05:00
Sub r squared over a.
05:01
So that would be negative one -half v .r squared over a.
05:11
And down here, we would get, nope, those don't cancel out.
05:21
My bad.
05:22
That would be negative 4 vr squared over a plus half of 4 vr squared over a.
05:45
So negative 4 plus 2 would be negative 2 vr squared over a.
05:57
Okay, so then the total distance that both of them travel would be negative 2 v .r squared over a.
06:04
Would be negative, and then i can factor out, well, okay, it's negative one -half plus negative two.
06:23
That would be negative five -halfs, vr squared over a.
06:32
So let's put that in a calculator.
06:40
Vr is 72 times 1 ,000 divided by 3 ,600.
06:54
Okay, a is negative 1.
07:02
So, negative 5 halves, vr squared over a would be 1 ,000 meters.
07:22
But they start out 950 meters apart.
07:28
So yes, there will be a collision.
07:37
If so, answer yes.
07:40
Give the speed of the red train and the speed of the green train at impact.
07:46
Okay.
07:48
So now we need the speeds at impact.
07:56
Well, let's figure out.
08:07
Okay, wait a minute, we need at impact.
08:11
So it's not going to make it to a thousand meters.
08:20
So i think what i'm going to do is i'm going to graph these, except i'm going to leave t in there.
08:45
So i'm going to graph, i'm going to add these together, and then i'm going to graph it.
08:59
So, vr, tr plus one half a, tr squared.
09:09
Vrtr plus one half a tr squared.
09:16
And then i want to add that to two vr.
09:20
R .t .g.
09:25
But i just want to change everything to t.
09:31
And i guess the time would be the same for all of them.
09:36
Well, technically not, but we'll see what happens here.
09:46
Vrt plus one half a t squared.
09:55
And then we've got two vrt plus one half a t squared.
10:05
Isn't it writing? t squared...