Name: Newton, Leibniz, and Usain Bolt | Derivatives introduction | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T11:54:47.000Z
Duration: 9 min 7 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

super famous British mathematician and physicist.

This is a picture of a Gottfried Leibnitz,

but maybe should be, famous German philosopher

and mathematician, and he was a contemporary of Isaac Newton.

And they did some of their-- most of their major work

And this right over here is Usain Bolt, Jamaican sprinter,

whose continuing to do some of his best work in 2012.

And as of early 2012, he's the fastest human alive,

and he's probably the fastest human that has ever lived.

And you might have not made the association with these three

You might not think that they have a lot in common.

But they were all obsessed with the same fundamental question.

And this is the same fundamental question

And the question is, what is the instantaneous rate

And in the case of Usain Bolt, how fast is he going right now?

Not just what his average speed was for the last second,

or his average speed over the next 10 seconds.

And so this is what differential calculus is all about.

Newton's actual original term for differential calculus

But it's all about what's happening in this instant.

And to think about why that is not a super easy problem

to address with traditional algebra, let's

I could have said d is equal to distance,

but we'll see, especially later on in calculus,

And so if we were to plot Usain Bolt's distance

capable of traveling 100 meters in 9.58 seconds.

can actually figure out his average speed.

Let me write it this way, his average speed

is just going to be his change in distance

And using the variables that are over here,

in y over change in x from this point to that point.

And this might look somewhat familiar to you

This is the slope between these two points.

If I have a line that connects these two points,

The change in distance is this right over here.

And our change in time is this right over here.

So our change in time is equal to 9.58 seconds.

Another way to think about it, the rise over the run you might

It's going to be 100 meters over 9.58 seconds.

And the slope is essentially just rate of change,

And you'll see, if you even just follow the units,

It would be velocity if we also specified the direction.

So let me get the calculator on the screen.

So we're going 100 meters in the 9.58 seconds.

So it's 10.4, I'll just write 10.4, I'll round to 10.4.

So it's approximately 10.4, and then the units

And just to have a concept of how fast this is,

If you wanted to know how many meters he's going in an hour,

Subtitles ListPlay Video

Newton, Leibniz, and Usain Bolt | Derivatives introduction | AP Calculus AB | Khan Academy

potential

extremely

figure

concept