Name: カークラッシュの計算 - Numberphile (Calculating a Car Crash - Numberphile)
Uploaded: 2021-01-14T10:46:32.000Z
Duration: 8 min 25 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

BEN SPARKS: Let's say, you're in Britain on a dual carriageway.

現在進行形

I'm gonna try and draw this. Two lanes, and we'll both go in this direction

and there's a blue car on the left, and it's going at 70 miles per hour

which is the legal limit on motorways and dual carriageways in this country.

BRADY HARAN: They're doing the right thing.

Trouble is, you could be doing the right thing, and other people on the roads might not.

There's a guy overtaking the blue car. It's gonna be the red car.

BEN: It's always the red car, and he's going faster.

In fact, I'm gonna draw him in at the moment he overtakes

and he's going -- as I'm sure it's happened to me, in the blue car I hasten to add

I've been in the blue car, and someone comes barreling past me going at 100 miles an hour.

Certainly it could happen, whether it's on a motorway or dual carriageway.

Now, they're not going the same speed, but there is a moment when they're neck-and-neck

and that's the moment I want to freeze time and ask you about what happens next.

Because at this moment when they're neck-and-neck, they see in front of them a tree

or some barrier which is unexpected, and so they both need to break

and we're going to assume lots of things, like is always the case with a mathematical question.

We have to model it to keep it simple enough to answer.

So the models here might be that, let's assume have same cars.

Let's assume reaction times are not part of this.

We could add those things in later if we want to complicate the model.

Let's assume they both slam on the brakes at the same time, and they break at the same rate

and by the time he gets there, the blue car has sort of just stopped in time.

So that's the blue car, who's got smaller apparently...

He has stopped with millimeters to spare, which is good.

BRADY: So the blue car just, just stops as it gets to the tree.

BEN: No crash for the blue guy. He slammed on the brakes just in time.

What I'm gonna claim, it's obvious that the red guy is in trouble.

The red guy is moving quicker. He brakes at the same time, at the same rate.

I think he's definitely gonna crash. No one seems to argue about whether the red guy's gonna crash.

What's really crucial, and here's the puzzle for you

is that, it matters what speed you crash at.

Right, if you crash at one mile an hour, no one's gonna really worry.

If you crash at a thousand miles an hour, you're in trouble.

Now, he's not gonna crash at thousand miles an hour. He's gonna crash slower because he started braking.

But, at what speed does he hit the tree? And that's the puzzle.

There's some intuition to get involved here, there's also some maths to check it out

and the answer is-- well, it surprised me.

BRADY: Alright. BEN: We're back! So the red guy has crashed.

I just feel like I missed my chance to draw a crash.

Because your intuition doesn't work well with speed questions

and this is why I got a bit surprised about this.

The first thing to notice is that, a lot of people think the answer is 30 miles an hour.

It's really 'sensible' to think about the difference in speed, which is 30 miles an hour at the start

and to think, if everything else is the same, surely that's the speed it's got left over.

There are lots of reasons why it's not correct, and one of the reasons you'll probably think is

I wouldn't be asking this question if it was 30, fine!

Another intuition thing to ask though, is

do you think it's slower than 30, or do you think it's quicker than 30?

Because if it's not 30, it's one of the two.

And I'm gonna tell you the answer, and I'm gonna justify it,

because when someone told me the answer, I just bawled. It was...

I was surprised. I was also a bit shocked and dare I say it, sobered

and maybe I changed my driving habits a little bit, because

assuming all that stuff we assumed, at approximately

He has not even reached the speed that the blue guy started braking at

There's the difference between not crashing at all, well done blue guy

and hitting a brick wall, or a tree in this case, at 71 miles an hour.

And that was from a difference of 30 miles an hour to start with, and everything else is the same.

So I think we should justify it before I leave you

to go and change your driving habits, and myself on my way home.

and maybe if you've solved it a certain way, try solve it another way.

You can use things called the SUVAT equations.

I've heard people make up nice rhymes to remember these things.

They're to do with constant acceleration equations to do with speed, distance, and time.

But there's another way which gets you the answer more quickly.

So maybe you should go and try this SUVAT thing

I'm gonna do lots of slightly dodgy things here

but you have to imagine that I'm just getting a ballpark for this model.

The kinetic energy for the blue guy is gonna be to do with several things.

There's a formula for kinetic energy, which looks like this.

There's a half in there for reasons I'm not going to go into

there's the mass of the car which we're going to assume is the same for both cars

Now, if we're gonna actually work out the kinetic energy

we'd work this out in meters per second, because that's the units that kinetic energy works in.

I'm just gonna dodge that. So I'm actually gonna say that it's kind of

kinetic energy is proportional to this, because I'm just gonna work with 70's.

because I'm gonna do the same with the red car so we can compare them.

So the blue guy has got ½m, whatever the m is, and we've got 70 squared.

That's its velocity in miles per hour, and we won't worry about it being in meter per second.

has a kinetic energy at the start of a ½m.

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カークラッシュの計算 - Numberphile (Calculating a Car Crash - Numberphile)

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