速度轉換 (英)

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速度轉換 (英) : 速度單位的轉換

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Welcome to the presentation on units.
Let's get started.
So if I were to tell you -- let me make sure my pen is set up
right -- if I were to tell you that someone is, let's say
they're driving at a speed of -- let's say it's Zack.
(Wait, where did my pen go? Oh, I was using the wrong tool.)
So let's say I have Zack.
And they're driving at a speed of, let me say,
twenty-eight feet per minute.
So what I'm going to ask you is if he's going twenty-eight feet in every
minute, how many inches will Zack travel in one second?
So how many inches per second is he going to be going?
Let's try to figure this one out.
So let's say if I had twenty-eight, and I'll write "ft" short for feet,
feet per minute, and I'll write "min" short for a minute.
So twenty-eight feet per minute, let's first figure out how many
inches per minute that is.
Well, we know that there are twelve inches per foot, right?
(And if you didn't know that you do now.)
So we know that there are twelve inches per foot.
So if he's going twenty-eight feet per minute, he's going to be going
twelve times that many inches per minute.
So, twelve times twenty-eight -- let's see. Let me do the little work down here --
twenty-eight times twelve is sixteen, fifty-six into two hundred and eighty.
(I probably shouldn't be doing it this messy.)
And this kind of stuff it would be OK to use a calculator,
although it's always good to do the math yourself.
It's good practice.
So that's six, five plus eight is thirteen.
three hundred and thirty-six.
So that equals three hundred and thirty-six inches per minute.
And something interesting happened here is that
you notice that I had a foot in the numerator here, and I had a
foot in the denominator here.
So you can actually treat units just the same way
that you would treat actual numbers or variables.
You have the same number in the numerator and you have the same
number in the denominator, and your multiplying not adding,
you can cancel them out.
So the feet and the feet canceled out and that's
why we were left with inches per minute.
I could have also written this as three hundred and thirty-six foot per minute
times inches -- that's "inches" -- inches per foot.
And -- and -- because the foot per minute came from here,
and the inches per foot came from here.
Then I'll just cancel this out and now I've got inches per minute.
So anyway, I don't want to confuse you too much
with all of that unit cancellation stuff.
The bottom line is you just remember, well if I'm going twenty-eight
feet per minute, I'm going to go twelve times that many inches
per minute, right, because there are twelve inches per foot.
So I'm going three hundred and thirty-six inches per minute.
So now I have the question, but we're not done, because the
question is how many inches am I going to be traveling
in one second.
So let me erase some of the stuff here at the bottom.
(Let me erase this...this is probably just going to confuse everybody.)
(Actually I'll erase this too.)
Ok.
So I'm going to be going...
So three hundred and thirty-six inches -- let's write it like that -- inches per minute,
and I want to know how many inches per second.
Well what do we know?
We know that one minute -- and notice, I write it in the
numerator here because I want to cancel it out with
this minute here.
one minute is equal to how many seconds?
It equals sixty seconds. Right?
And this part can be confusing, but it's always good to just
take a step back and think about what I'm doing.
If I'm going to be going three hundred and thirty-six inches per minute, how many
inches am I going to travel in one second?
Am I going to travel more than three hundred and thirty-six or am I going
to travel less than three hundred and thirty-six inches per second.
Well obviously less, because a second is a much
shorter period of time.
So if I'm in a much shorter period of time, I'm going
to be traveling a much shorter distance,
if I'm going the same speed.
So I should be dividing by a number, which makes sense.
I'm going to be dividing by sixty.
I know this can be very confusing at the beginning, but
that's why I always want you to think about should I be getting
a larger number or should I be getting a smaller number and
that will always give you a good reality check.
And if you just want to look at how it turns out in terms of
units, we know from the problem that we want this minutes to
cancel out with something and get into seconds.
So if we have minutes in the denominator in the units here,
we want the minutes in the numerator here, and the seconds
in the denominator here.
And one minute is equal to sixty seconds.
So here, once again, the minutes and the
minutes cancel out.
And we get three hundred and thirty-six over sixty inches per second.
[coughs] (Excuse me.)
Now if I were to actually divide this out, we could see --
actually we could just divide the numerator and the denominator by six.
six goes into three hundred and thirty-six, what, fifty-six times?
fifty-six over ten, and then we can divide that again by two.
So then that gets us twenty-eight over five.
And twenty-eight over five -- let's see, five goes into twenty-eight five times, twenty-five.
Three, five point six.
So this equals 5.6.
So I think we now just solved the problem.
If Zack is going twenty-eight feet in every minute, that's his
speed, he's actually going 5.6 inches per second.
Hopefully that kind of made sense.
Let's try to see if we could do another one.
If I'm going ninety-one feet per second, how many miles
per hour is that?
Well, ninety-one feet per second.
So how many -- If we want to say how many miles that is, should we be
dividing or should we be multiplying?
We should be dividing because it's going to be a
smaller number of miles.
And we know that one mile is equal to -- and you might want to just
memorize this -- five thousand, two hundred and eighty feet.
It's actually a pretty useful number to know.
And then that will actually cancel out the feet.
Then we want to go from seconds to hours, right?
So, if we go from seconds to hours, if I can travel ninety-one feet
per second, how many will I travel in an hour, I'm going to
be getting a larger number because an hour's a much larger
period of time than a second.
And how many seconds are there in an hour?
Well, there are three thousand, six hundred seconds in an hour.
sixty seconds per minute and sixty minutes per hour.
So three thousand, six hundred over one seconds per hour.
And these seconds will cancel out.
Then we're just left with, we just multiply everything out.
We get in the numerator, ninety-one times thirty-six hundred, right?
ninety-one times one times thirty-six hundred.
In the denominator we just have five thousand, two hundred and eighty.
This time around I'm actually going to use a calculator --
let me bring up the calculator just to show you that I'm
using the calculator.
Let's see, so if I say ninety-one times thirty-six hundred, Woops! I messed up.
(carefully) Ninety-one times thirty-six hundred. that equals a huge
number divided by five thousand, two hundred and eighty.
(Oh, man. I keep messing up.) [More errors.] This calculator -- I think my mouse is messed up. Let me see if I can type it.
91 times 3,600 divided by 5,280 -- 62.05!
So that equals 62.05 miles per hour.

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