00:01
So in this problem we are looking at stopping distance.
00:03
So the sober driver takes 0 .41 seconds to react.
00:12
If we start with say some x equals zero here, they're going to cover some distance d1 in that time, traveling at our initial velocity v0 of 63 .6 miles per hour.
00:31
Then the drunk driver covers a longer distance before they start and hit the brakes of 1 .12 seconds.
00:41
This is going to be distance 2.
00:44
And what we want to do is find the difference in stopping distance.
00:47
So we want to find this distance here d.
00:53
So from the drawing here we see that d2 is d plus d1 or d is therefore d2 minus d1.
01:03
Now what is the distance? this is where we're going to look at our kinematics.
01:09
We have a constant velocity because the stopping hasn't happened yet.
01:13
We are dealing with reaction time.
01:15
So this is x equals zero, t equals zero.
01:18
They continue at the constant velocity v until they start hitting the brakes.
01:24
And for a constant velocity we have that x is v times t.
01:30
And our x is our distances here of course.
01:33
And so we can use that then to find d.
01:35
Now we need to convert the velocity into meters per second.
01:42
63 .6 miles per hour, 5280 feet in a mile, 12 inches in a foot, and then 0 .0254 meters in an inch based on the definition of an inch being 2 .54 centimeters exactly.
02:08
And then 3600 seconds in a minute.
02:15
So because all of the, or not in a minute of course, in an hour.
02:20
And so of course all of these fractions we multiplied are equivalent.
02:24
They're equal to one...