So, lets figure out the final velocity, the vertical and horizontal components of that final velocity, and then we can reconstruct the total final velocity.

This is my final velocity.

The average velocity is just the initial velocity plus the final velocity over 2.

The average velocity is just the average of the initial velocity and the final velocity.

It is our final vertical velocity, minus our initial vertical velocity.

The height here is my final velocity minus my initial velocity.

Our final velocity is 60 mph.

So this is his final velocity.

So that equals 5.25. plus 49.85 times the skater's velocity, the final velocity.

What do we know about final velocity?

So our final velocity is 60 mph.

What's going to be his final velocity?

We know also that velocity, or let's say the change in velocity, is equal to the final velocity minus the initial velocity.

Now, what is the average velocity here? It's going to be our final velocity, plus our initial velocity, over 2. It's just the average of the initial and final.

If his initial velocity is negative 5 feet per second, his final velocity is this.

We know that the final velocity is equal to the initial velocity plus acceleration times time.

No. we know acceleration, but don't know final velocity.

So that is the magnitude of our final velocity.

We know the average velocity is equal to the final velocity plus the initial velocity over 2, and this assumes acceleration is constant.

So that is the magnitude of our total final velocity.

My final velocity over here has to be 260 km hour.

So in this situation, our final velocity is 13 m s,

We have distance is equal to the initial velocity plus the final velocity, so let's substitute this expression right here.

And the average velocity...if your acceleration is constant... if and only if your acceleration is constant then your average velocity will be the average of your final velocity and your initial velocity and so in this situation, what is our average velocity? well our average velocity, let's do it in m s is going to be our final velocity, which is (let me calculate it down here) so our average velocity in this example

So we get, our change, our final velocity is 26.03 ill say.

The initial velocity, plus, now the final velocity is now the initial velocity, plus acceleration times time, and then we divide all of that by 2 times time.

Final velocity is minus 100 meters per second, and then the initial velocity is 0, so the change in velocity is equal to minus 100 meters per second.

And we know a way of figuring out our final velocity from the initial velocity, given our time in the air.

So this is interesting, the distance we traveled is equal to 1 2 of the initial velocity plus the final velocity.

And so we can solve for the vertical component of our final velocity.

What is neat about this, is that we have our final velocity vector.

What an average velocity is, is some velocity and in this case it's exactly right between our two... our final and initial velocities

We're given the acceleration, we're given the initial velocity, and I asked you how do we figure out what the final velocity is?

But if you do have a constant acceleration like this, you can assume that the average velocity is going to be the average of the initial velocity and the final velocity.

This hopefully is intuitive to you, that the change is just the final velocity minus the initial velocity, and that that equals acceleration times time.

And so this is V_f, this is my final velocity and what would it be?

So my final velocity is going to be right over there (I'll write it down here because it's getting in the way of this word velocity)

I know my initial velocity, I know my final velocity, right before I hit the ground or right when I hit the ground, what's the distance?

If we do, then it just turns out to the final distance is equal to the average velocity times the final time, but

So all I did here is I converted the take off velocity, so this is 72 m s, this has to be the final velocity after accelerating.

So these two terms this term and this term will simplify to 1 2 Vi, 1 2 the initial velocity plus 1 2 times the final velocity.

So this is the 1 2, so plus 1 2 times our final velocity minus 1 2 times our initial velocity (I want to do that in blue.

That is the magnitude of our final velocity, but we also need to figure out its direction.

Velocity_average in this example... is going to be our final example...78 m s plus our initial velocity,.

That's our average velocity, velocity average.