Placeholder Image

字幕列表 影片播放

  • In this video, I want to talk a little bit about acceleration.

    在這影片中,我要討論一些加速度的問題

  • And this is probably an idea that you're

    在這影片中,我要討論一些加速度的問題

  • somewhat familiar with, or at least

    你們可能對這個有點熟悉

  • you've heard the term used here or there.

    你可能有聽過它

  • Acceleration is just the change in velocity over time.

    或者你有聽過這個名詞

  • Probably one of the most typical examples of acceleration,

    加速度就是隨時間改變的速度

  • if you're at all interested in cars,

    如果你對車有興趣

  • is that many times they will give you

    最典型的加速度就是

  • acceleration numbers, especially for sport cars, actually

    它常常會告訴你加速度是多少

  • all cars if you look up in Consumer Reports,

    它常常會告訴你加速度是多少

  • or wherever they give the stats on different cars.

    特別是賽車,實際上

  • They'll tell you something like, I don't know, like a Porsche--

    所有車如果看一下消費者指南

  • and I'm going to make up these numbers right over here.

    或他給你不同車的統計

  • So let's say that we have a Porsche 911.

    他們會告訴你像保時捷(我不知道)

  • They'll say that a Porsche 911, they'll literally measure it

    我要編造一下數據

  • with a stopwatch, can go 0 to 60 miles per hour.

    假設有一台保時捷911

  • And these aren't the exact numbers,

    由碼表測量

  • although I think it's probably pretty close.

    每小時可從0至60英里

  • 0 to 60 miles per hour in, let's say, 3 seconds.

    每小時可從0至60英里

  • So, although officially what they're giving you right here

    這不是適確切的數字

  • are speeds, because they're only giving you

    儘管我認為很接近

  • magnitude and no direction, you can

    我們說三秒,每小時從0至60英里

  • assume that it's in the same direction.

    我們說三秒,每小時從0至60英里

  • I mean, We could say, 0 miles per hour

    儘管官方給的是速率

  • to the east to 60 miles per hour to the east in 3 seconds.

    只有大小沒有方向

  • So what was the acceleration here?

    只有大小沒有方向

  • So I just told you the definition of acceleration.

    你可以假設方向不變

  • It's change in velocity over time.

    我指的是我們可以說

  • So the acceleration-- and once again acceleration

    向東三秒之內從0mph加速到60mph

  • is a vector quantity.

    所以加速度是多少?

  • You want to know not only how much is velocity changing

    我剛告訴你們加速度的定義

  • over time, you also care about the direction.

    是單位時間內速度的變化量

  • It also makes sense because velocity

    所以加速度同樣是向量

  • itself is a vector quantity.

    所以加速度同樣是向量

  • It needs magnitude and direction.

    你不只要知道速度的變化

  • So the acceleration here-- and we're

    你也要在乎方向

  • just going to assume that we're going

    因為速度

  • to the right, 0 miles per hour and 60 miles per hour

    本身是向量

  • to the right-- so it's going to be change in velocity.

    需要大小和方向

  • So let me just write it down with different notation

    所以這裡的加速度

  • just so you could familiarize yourself

    我們假設向右行駛

  • if you see it in the textbook this way.

    從0mph至60mph

  • So change in velocity.

    速度將會變化

  • This delta symbol right here just means "change in."

    讓我寫不同的符號

  • Change in velocity over time.

    這樣你可能比較習慣

  • It's really, as I've mentioned in previous videos,

    當你在教科書看到

  • it's really time is really a change in time.

    速度的變化

  • But we could just write time here.

    △是"變化"

  • This 3 seconds is really change in time.

    隨時間改變的速度

  • It might have been, if you looked at your second hand,

    我在影片前提到

  • it might have been 5 seconds when it started, and then my 8

    在時間內改變

  • seconds when it stopped, so it took a total of 3 seconds.

    但我們在這裡寫成時間

  • So time is really a change in seconds.

    在三秒內改變

  • But we'll just go with time right here, or just with a t.

    如果你看一下秒針

  • So what's our change in velocity?

    從五秒開始到第八秒停止

  • So our final velocity is 60 miles per hour.

    總共花費三秒

  • And our original velocity was 0 miles per hour.

    所以時間實際上是過多少秒

  • So it's 60 minus 0 miles per hour.

    讓我們用"t"來代替時間

  • And then, what is our time?

    所以速度變化量是多少

  • What is our time over here?

    我們最終速度是60mph

  • Well, our time is, or we could even say our change in time,

    我們最終速度是60mph

  • our change in time is 3 seconds.

    起始速度是0mph

  • So this gives us 20 miles per hour, per second.

    所以是(60-0)mph

  • Let me write this down.

    那我們的時間呢

  • So this becomes, this top part is 60.

    這裡的時間是多少

  • 60 divided by 3 is 20.

    或者說 改變的時間是

  • So we get 20.

    改變的時間是3秒

  • But then the units are little bit strange.

    改變的時間是3秒

  • We have miles.

    所以得到每秒20mph

  • Instead of writing MPH, I'm going to write miles per hour.

    我把這寫下來

  • That's the same thing as MPH.

    這變成上面的60

  • And then we also, in the denominator, right over here,

    60/3=20

  • have seconds.

    所以得到20

  • Which is a little bit strange.

    但單位有一點奇怪

  • And as you'll see, the units for acceleration

    我們有英里

  • do seem a little bit strange.

    代替成mph我要寫成每小時英里

  • But if we think it through, it actually

    這和mph是相同的

  • might make a little bit of sense.

    在分母的地方

  • So miles per hour.

    有秒

  • And then we could either put seconds like this,

    這有一點奇怪

  • or we could write per second.

    就你所看到的 加速的單位

  • And let's just think about what this is saying,

    看起來有點奇怪

  • and then we could get it all into seconds,

    但如果想一想他的運動過程

  • or we could all get into hours, whatever we like.

    這其實說得通

  • This is saying that every second, this Porsche 911

    所以mph

  • can increase its velocity by 20 miles per hour.

    我們也可以把秒寫成這樣

  • So its acceleration is 20 miles per hour, per second.

    或是寫成每秒

  • And actually, we should include the direction,

    我們來想剛才說的東西

  • because we're talking about vector quantities.

    我們都可以用秒

  • So this is to the east.

    或者小時哪個都行

  • So this is east, and then this is east right over here--

    保時捷911每秒

  • just so we make sure that we're dealing with vectors.

    可以將速度增加20mph

  • You're giving it a direction, due east.

    所以加速度是20miles/hr*s

  • So every second it can increase in velocity

    實際上 我們要加上方向

  • by 20 miles per hour.

    因為我們討論的是向量

  • So hopefully, with the way I'm saying it,

    所以這是向東

  • it makes a little bit of sense.

    所以這是向東

  • 20 miles per hour, per second.

    我們可以確定的是我們是在講向量

  • That's exactly what this is talking about.

    你給定一個方向 向東

  • Now we could also write it like this.

    所以每秒他的速度增加

  • This is the same thing as 20 miles per hour,

    20mph

  • because if you take something and you

    希望我所說的可以

  • divide by seconds, that's the same thing as multiplying it

    讓你有感覺

  • by 1 over seconds.

    20miles/hr*s

  • So that's miles per hour-seconds.

    這就是我們討論的

  • And although this is correct, to me

    我們也可以寫下

  • this makes a little less intuitive sense.

    每小時20英里

  • This one literally says it.

    因為當你有一些東西然後你

  • Every second, it's increasing in velocity by 20 miles per hour.

    除以秒 相當於每1秒

  • 20 miles per hour increase in velocity per second.

    增加多少

  • So that kind of makes sense to me.

    那是 miles/hr*s

  • Here it's saying 20 miles per hour-seconds.

    那是 miles/hr*s

  • So once again, it's not as intuitive.

    雖然是正確的 但對我來說

  • But we can make this so it's all in one unit of time,

    少一點直覺的感覺

  • although you don't really have to.

    從字面上來說

  • You can change this so that you get rid

    每秒速度增加20mph

  • of maybe the hours in the denominator.

    每秒速度增加20mph

  • And the best way to get rid of an hour in the denominator,

    這對我來說比較有感覺

  • is by multiplying it by something

    在這裡說20miles/hr*s

  • that has hours in the numerator.

    同樣的 我沒感覺

  • So hour and seconds.

    我們可以讓時間的單位一致

  • And here, the smaller unit is the seconds.

    雖然你不必

  • So it's 3,600 seconds for every 1 hour.

    你可以把

  • Or 1 hour is equal to 3,600 seconds.

    分母上的小時消掉

  • Or 1/3600 of an hour per second.

    最好去掉分母上小時的方法是

  • All of those are legitimate ways to interpret

    乘以一個分子上有小時的數

  • this thing in magenta right over here.

    乘以一個分子上有小時的數

  • And then you multiply, do a little dimensional analysis.

    所以小時和秒

  • Hour cancels with hour.

    在這裡比較小的單位是秒

  • And then will be equal to 20/3600.

    一小時有3600秒

  • 20/3600 miles per seconds times seconds.

    或一小時等於3600秒

  • Or we could say, miles-- let me write

    或一小時的1/3600是1秒

  • it this way-- miles per seconds times seconds.

    所以這些洋紅色的字都是相同的意思

  • Or we could say, miles per second-- I

    所以這些洋紅色的字都是相同的意思

  • want to do that in another color-- miles

    然後相乘 做一點單位的分析

  • per second squared.

    小時跟小時消掉

  • And we can simplify this a little bit.

    會等於20/3600

  • Divide the numerator and denominator by 10.

    20/3600 miles/s*s

  • You get 2/360.

    或者說 讓我寫下英里

  • Or you could get, this is the same thing

    miles/s*s

  • as, 1/180 miles per second squared.

    或者說每秒英里

  • And I'll just abbreviate it like that.

    我換另一個顏色

  • And once again, this 1/180 of a mile, how much is that?

    每秒平方分之英里

  • You might want to convert to feet.

    每秒平方分之英里

  • But the whole point in here is, I just

    我們可以化簡一下

  • wanted to show you that, well, one, how

    讓分子和分母都除以10

  • do you calculate acceleration?

    得到2/360

  • And give you a little bit of a sense of what it means.

    或者和1/180一樣

  • And once again, this right here, when

    1/180 miles/s^2

  • you have seconds squared in the bottom of your units,

    我這樣縮寫

  • it doesn't make a ton of sense.

    同樣的 1/180英里 是多少?

  • But we can rewrite it like this up here.

    你可能想用英尺表示

  • This is 1/180 miles per second.

    但重點是

  • And then we divide by seconds again, per second.

    我只想給你們知道

  • Or maybe I can write like this, per second,

    怎麼計算加速度

  • where this whole thing is the numerator.

    讓你們體會它的意義

  • So this makes a little bit more sense

    同樣的在這

  • from an acceleration point of view.

    當你分母的單位是s*s

  • 1/180 miles per second, per second.

    那沒有感覺

  • Every second, this Porsche 911 is

    我們寫成上面那樣

  • going to go 1/180 of a mile per second faster.

    1/180 miles/s

  • And actually, it's probably more intuitive

    再除以時間(每秒)

  • to stick to the miles per hour, because that's something

    或者可以寫成這樣

  • that we have a little bit more sense on.

    把整個寫成分數

  • And another way to visualize it.

    這樣從加速度的觀點來看

  • If you were to be driving that Porsche,

    比較有感覺

  • and you were to look at the speedometer for that Porsche,

    1/180 miles/s/s

  • and if the acceleration was constant--

    每秒 保時捷911

  • it's actually not going to be completely constant--

    增加1/180 miles/s

  • and if you look at speedometer-- let me draw it.

    實際上 如果用每小時英里

  • So this would be 10, 20, 30, 40, 50, 60.

    會更直觀

  • This is probably not what the speedometer for a Porsche

    因為我們對這個比較有感覺

  • looks like.

    另一種方式去想像

  • This is probably more analogous to a small four cylinder car's

    如果你們開著保時捷

  • spectrometer.

    看著保時捷的車速表

  • I suspect the Porsche's speedometer goes much

    如果加速度是固定的

  • beyond 60 miles per hour.

    事實上不會完全不變

  • But what you would see for something

    如果你看著車速表 讓我來畫一下

  • accelerating this fast is, right when you're starting,

    應該是10 20 30 40 50 60

  • the speedometer would be right there.

    這可能像是保時捷的車速表

  • And that every second it would be 20 miles per hour faster.

    這可能像是保時捷的車速表

  • So after a second the speedometer

    這可能類似四汽缸汽車

  • would have moved this far.

    的車速表

  • After another second the speedometer

    我猜保時捷的車速表

  • would have moved this far.

    會超過60mph

  • And then after another second the speedometer

    你可能會看到

  • would have moved that far.

    如果一輛車加速度那麼大,當你開始時

  • And the entire time you would have kind of

    車速表在這

  • been pasted to the back of your seat.

    每過一秒應該就變快20mph

In this video, I want to talk a little bit about acceleration.

在這影片中,我要討論一些加速度的問題

字幕與單字

單字即點即查 點擊單字可以查詢單字解釋