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We will discuss velocities and acceleration.

I'll start with something simple.

I have a motion of an object along a straight line —

we'll call that one-dimensional motion.

And I'll tell you that the object is here at time t1.

At time t2, it's here.

At time t3, it's there.

At time t4, it's here and at time t5, it's back where it was at t1.

And here you see the positions in x where it is located at that moment in time.

I will define this to be the increasing value of x.

It's my free choice, but I've chosen this now.

Now we will introduce what we call the average velocity.

I put a bar over it.

That stands for average between time t1 and time t2.

That we define in physics as x at time t2 minus x at time t1 divided by t2 minus t1.

That is our definition.

In our case, because of the way that I define the increasing value of x, this is larger than 0.

However, if I take the average velocity between t1 and t5 that would be 0, because they are at the same position so the upstairs is 0.

If I had chosen t4 and t2 —

average velocity between time t2 and t4 —

you would have seen that that is negative because the upstairs is negative.

Notice that I haven't told you where I choose my zero on my x axis.

It's completely unimportant for the average velocity.

It makes no difference.

However, if I had chosen this to be the direction of increasing x then, of course, the signs would flip.

Then this would have been negative and this would have been positive.

So the direction, that you are free to choose determines the signs.

The location where you put your zero is not important but signs in physics do matter.

Signs are important.

Whether you owe me money or I owe you money the difference is only a minus sign but I think it's important for you.

Now I will give you not only the positions —

as I did here on the x axis at discrete moments in time —

but I'm going to tell you exactly where the object is at any moment in time.

Here you see an xt diagram so you see that at t1, the object is at position xt1.

This is the road of the object.

This is the straight line, where it's moving.

It starts here and it goes to this position.

It goes to this one, it comes back to t4 and it comes back here.

I will tell you now every moment in time in between.

And there it goes.

Voila.

This is now information that is way more.

You have the information at any moment in time.

Notice that I now did choose x = 0.

I chose it somewhere here but I could have chosen it at any other point —

for whatever follows you will see that it makes no difference —

so I have chosen a zero point so that I can make a graph.

And now we will look at the average velocity in a somewhat different way.

Say I choose my time t2 and t3.

I draw here now this line.

And this angle I call alpha and this part here I call delta x and this here is delta t.

And so you could right now —

if you're careful about your sign convention —

you could write down now that the average velocity equals delta x divided by delta t.

But be careful.

If the angle is positive —

I call this a positive angle —

then the average velocity is positive but if I have a negative angle then the average velocity would be negative.

For instance, between t4 and t5, if I draw this line then this angle here is negative and so the average velocity between t4 and t5 is now negative.

I'll start with something simple.

I have a motion of an object along a straight line —

we'll call that one-dimensional motion.

And I'll tell you that the object is here at time t1.

At time t2, it's here.

At time t3, it's there.

At time t4, it's here and at time t5, it's back where it was at t1.

And here you see the positions in x where it is located at that moment in time.

I will define this to be the increasing value of x.

It's my free choice, but I've chosen this now.

Now we will introduce what we call the average velocity.

I put a bar over it.

That stands for average between time t1 and time t2.

That we define in physics as x at time t2 minus x at time t1 divided by t2 minus t1.

That is our definition.

In our case, because of the way that I define the increasing value of x, this is larger than 0.

However, if I take the average velocity between t1 and t5 that would be 0, because they are at the same position so the upstairs is 0.

If I had chosen t4 and t2 —

average velocity between time t2 and t4 —

you would have seen that that is negative because the upstairs is negative.

Notice that I haven't told you where I choose my zero on my x axis.

It's completely unimportant for the average velocity.

It makes no difference.

However, if I had chosen this to be the direction of increasing x then, of course, the signs would flip.

Then this would have been negative and this would have been positive.

So the direction, that you are free to choose determines the signs.

The location where you put your zero is not important but signs in physics do matter.

Signs are important.

Whether you owe me money or I owe you money the difference is only a minus sign but I think it's important for you.

Now I will give you not only the positions —

as I did here on the x axis at discrete moments in time —

but I'm going to tell you exactly where the object is at any moment in time.

Here you see an xt diagram so you see that at t1, the object is at position xt1.

This is the road of the object.

This is the straight line, where it's moving.

It starts here and it goes to this position.

It goes to this one, it comes back to t4 and it comes back here.

I will tell you now every moment in time in between.

And there it goes.

Voila.

This is now information that is way more.

You have the information at any moment in time.

Notice that I now did choose x = 0.

I chose it somewhere here but I could have chosen it at any other point —

for whatever follows you will see that it makes no difference —

so I have chosen a zero point so that I can make a graph.

And now we will look at the average velocity in a somewhat different way.

Say I choose my time t2 and t3.

I draw here now this line.

And this angle I call alpha and this part here I call delta x and this here is delta t.

And so you could right now —

if you're careful about your sign convention —

you could write down now that the average velocity equals delta x divided by delta t.

But be careful.

If the angle is positive —

I call this a positive angle —

then the average velocity is positive but if I have a negative angle then the average velocity would be negative.

For instance, between t4 and t5, if I draw this line then this angle here is negative and so the average velocity between t4 and t5 is now negative.

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