00:01
Okay, so for this problem, we have a train that is starting from rest and right.
00:08
When it starts from rest, a car goes driving by it.
00:13
So a couple things happen here.
00:15
First of all, since the train is starting from rest, we know its initial velocity is zero meters per second.
00:22
Now the train is accelerating as it travels down the track, and it travels down that track 4 28 seconds.
00:35
Yeah.
00:37
Um, the car is traveling at a constant velocity, meaning its acceleration is zero meters per second squared.
00:45
Um, and at 28 seconds, the train has actually caught up to the car and driven far enough that the front of the train and the car are at the same position again.
00:57
So at this point in time, both the train and the car have gone acts in terms of their distance.
01:04
They've both traveled that far.
01:08
Okay, now, the first part of this problem is asking us to find the velocity of the car.
01:12
How fast the car has to be traveling for this scenario to pan out.
01:17
Um, so for that, i'm going to find a few variables.
01:20
I don't know what the blast of the car is right now.
01:22
So i'm in call that the sub sea for the velocity of the car.
01:27
Um and then from there, we also don't know what the acceleration of the train is.
01:34
So i'm going to call that acceleration of the train.
01:39
Okay, so that's kind of our starting information that we have.
01:43
But this problem actually gives us quite a bit more in terms of starting information.
01:49
So that's what's going on 28 seconds after it begins driving.
01:53
But we actually know a bit more about that as well, because halfway through the travel, you dropped two more of these in here for us to work with halfway through the travel, the train or the car is a bit ahead of the train.
02:14
So when we are halfway there, here's the train.
02:22
And here is the car, um, are starting conditions the same zero meters per second.
02:28
Um, the train has an acceleration of tea, but now we're looking what's happening 14 seconds after the start.
02:36
So the time for both of these is 14 seconds.
02:39
Um, acceleration of car still zero.
02:41
And this is still velocity there.
02:43
So halfway through the time frame.
02:46
The car is halfway to x, but the train is a little bit behind that the car has actually moved from beyond the back of the train.
02:56
Is it up towards the front? the train is only gone half of x minus 92.
03:02
It is trailing a little bit.
03:06
So these two situations let us kind of cobble together a couple different equations that we can work with to solve this problem.
03:14
So let's look at our first equation.
03:17
The car is pretty basic, so let's start with an equation for the velocity of the car equation.
03:25
One for the velocity of the car.
03:29
The velocity of the car is equal to the distance...