00:01
Okay, you're driving your car on a country road at 21 .5 meters per second.
00:06
And as you come over a hill you see a tractor 35 .7 meters in front of you, moving at 10 meters per second in the same direction.
00:19
So you slam on your brakes, slow down at 7 meters per second squared for your acceleration.
00:24
Will you hit the tractor before you stop? how far will you travel before you stop or collide with the tractor? and if you do stop, how far is the tractor in front of you? when you stop.
00:37
So you have a car here and you got a tractor.
00:45
That's a tractor.
00:52
There's your tractor, right? okay, so the car is moving, let's call it with speed v car initial.
01:00
And the tractor is moving with speed, it's constant speed, so we'll just call it v tractor, right? and let's set the origin right here.
01:09
So x equals zero is that line.
01:15
Um, so the tractor is initially at x equals, uh, call it d, 35 .7 meters.
01:30
So let's tackle the first part.
01:32
Will you hit the tractor before you stop? so let's just see how far you travel.
01:38
So let's use v car final squared equals v car initial squared plus two acceleration times x final minus x initial.
01:52
So the final speed of the car is zero.
01:55
We know the acceleration is negative, so i'm going to denote that with a negative here.
02:03
So minus 2a times x final because x initial for the car is zero.
02:10
So what's the final position of the car? it's equal to the initial speed squared divided by two times its acceleration.
02:18
Okay, so the final position of the car when it stops is 33 .02 meters.
02:25
Okay, so even if the tractor wasn't moving, you would still be okay because the car stops, you know, like right there.
02:32
So that was, that was kind of nice.
02:38
We didn't have to factor in the movement of the tractor...