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

Acceleration.

And this is probably an idea that you are somewhat familiar with

or at least you've heard the term used here or there.

Acceleration is just the change in velocity over time.

Change in velocity over time.

Probably one of the most typical examples of acceleration, if you are at all interested in cars

is that many times they will give you acceleration numbers

especially for sport cars.

Actually all cars, if you look up in consumer reports or wherever they give stats on different cars

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

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

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

They'll say that a Porsche 911 -they'll literally measure it with a stopwatch -

can go 0 to 60 miles per hour -

and these aren't the exact numbers, although I think it's probably pretty close.

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

In three seconds.

So although officially what they are giving you right here are speeds

cause they are only giving you magnitude and no direction,

you can assume that it's in the same direction.

And you can say 0 mph to the East to 60 mph to the East in 3 seconds,

so what was the acceleration here?

So I just told you the definition of acceleration -

it's the change in velocity over time!

So the acceleration, and once again, acceleration is a vector quantity.

You want to know not only how much is velocity changing over time,

you also care about the direction!

It also makes sense because the velocity itself is a vector quantity.

Needs magnitude AND direction.

So the acceleration here,

and we are just going to assume that we are going to the right,

0 mph and 60 mph to the right.

So what is... It's going to be change in velocity - let me just write it down with different notation,

just so you can familiarise yourself if you see it in a textbook this way.

So change in velocity. This delta symbol right here just means 'change in'.

Change in velocity over time. Over time.

And it's really, as I've mentioned in previous videos,

time, it's really change in time, but we can just write time here.

This 3 seconds is really change in time.

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

it might have been 5 seconds when it started and it might have been 8 seconds

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

So time - it's really a change in seconds. But we'll just go with time right here,

Or we'll go with 't'.

So what's our change in velocity?

So our final velocity is 60 mph.

Our final velocity is 60 mph.

And our original velocity was 0 mph,

so it's 60 minus 0 mph.

And then what is our time?

What is our time over here?

Well, our time is, or we could even say

our change in time,

our change in time is 3 seconds.

3 seconds.

So this gives us 20 mph per second.

Let me write this down.

So this becomes... This top part is 60.

60 divided by 3 is 20.

So we get 20... but then the units are a little bit strange.

We have miles... Instead of writing mph

I'm going to write miles per hour.

That's the same thing as mph.

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

we also, right over here in the denominator

have seconds.

Which is a little bit strange.

And, as you'll see, the units for acceleration do seem a little strange.

But if we think it through, it actually might make a bit of sense.

So miles per hour, and then we can either put seconds,

like this, or we can write per second.

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

and then we can get it all into seconds, or hours, whatever you like.

This is saying that every second, this Porsche 911

can increase its velocity by 20 mph.

So its acceleration is 20 miles per hour per second.

And actually we should include a direction, cause we're talking about vector quantities.

So this is to the east.

And this is east right over here.

Just so we make sure that we're dealing with vectors.

You're giving it a direction. Due east.

So every second, it can increase its velocity by 20 mph.

So hopefully, the way I'm saying it makes a little bit of sense.

20 miles per hour per second.

That's exactly what this is talking about.

Now, we can also write it like this, this is the same thing

as 20 miles per hour...

Cause if you take something and divide it by second,

that's the same thing as multiplying it by 1 over second.

So that's miles per hour seconds.

And although this is correct, to me this makes a little less intuitive sense.

This one literally says that every second

it's increasing in velocity by 20 miles per hour.

20 miles per hour increase in velocity per second.

So that kind of makes sense to me.

Here it's saying 20 miles per hour seconds.

So once again, it's not as intuitive.

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

Althought you don't really have to.

You can change this so you can get rid of

maybe the hours in the denominator.

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

is by multiplying it by something that has hours in the numerator.

So hour, and seconds. And here...

The smaller units are seconds, so it's 3600 seconds for every 1 hour.

Or, one hour is equal to 3600 seconds.

Or, 1/3600 of an hour per second.

All of those are legitime ways to interpret this thing in magenta right over here.

And then you multiply.

Do a little dimensional analysis.

Hour cancels with hour, and then you have...

This will be equal to...

This will be equal to 20/3600.

20/3600.

Miles per seconds times seconds.

Or we could say, miles... Let me write it this way.

Miles per seconds times seconds.

Or you could say, miles per second...

I want to do that in another colour.

Miles per second squared.

Miles per seconds... Miles per second squared.

And we can simplify this a little bit.

Divide the denominator and numerator by ten.

You get 2 over 360.

Or you could get.. This is the same thing as 1 over... 1 over 180.

Miles per second squared. Per second squared.

I'll just abbreviate like that.

And once again, this doesn't make...

1 180th of a mile. How much is that?

You might want to convert it to feet,

but the whole point here is,

I just wanted to show you that

well, one, how do you calculate acceleration,

and give you a little bit of sense what it means.

And once again, what you have here,

when you have seconds squared in the bottom of the units,

it doesn't make a ton sense, but we could rewrite it like this up here.

This is 180... or 1 / 180 miles per second...

and then we divide by seconds again: per second.

Or maybe I can write it like this; per second.

Where this whole thing is the numerator.

So this makes a little bit more sense from an acceleration point of view.

One over 180 miles per second...

Every second this Porsche 911 is going

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

And actually it's probably more intuitive to stick to the miles per hour,

cause that's something that we have a little bit more sense on.

And another way to visualize it.

Another way to visualize it.

If you were driving that Porsche, and

you were looking at the speedometer of that Porsche,

and if the acceleration was constant,

it's actually not going to be completely constant,

and if you looked at this speedometer...

Let me draw it,

so this would be 10, 20, 30, 40, 50, 60.

This is probably not what the speedometer for a Porsche looks like,

this is probably more analogous to a small

four cylinder car's speedometer, I suspect

the Porsche's speedometer goes much beyond

60 mph, but you would see, for something

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

the speedometer would be right there.

And then every second, it would be 20 mph faster.

So after a second, the speedometer would have moved this far.

After another second, the speedometer would have moved this far.

And then after another second, the speedometer would have moved that far.

And the entire time you would have kind of been pasted to the back of your seat.

Is that compulsory to represent arrow on the acceleration symbol?