FlNAL VELOClTY SQUARED, FlNAL VELOClTY TlME FlNAL VELOClTY

Vi plus Vf (No that's not the right color)

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.

This is my final velocity.

CHANGE IN VELOClTY IS THE SAME THlNG AS FlNAL VELOClTY MlNUS INlTIAL VELOClTY

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

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.

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

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

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

IS EQUAL TO OUR FlNAL VELOClTY SQUARED

What do we know about final velocity?

Our final velocity is 60 mph.

So this is his final velocity.

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

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

INSTEAD OF WRlTING CHANGE IN VELOClTY, WE CAN JUST WRlTE FlNAL VELOClTY

IT WlLL BE EQUAL TO FlNAL VELOClTY SQUARED

YOU WlLL GET, AND I FLlP THEM AROUND, FlNAL VELOClTY IS EQUAL TO

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)

And so that will tell me how fast I've gone

So that is the magnitude of our 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.

NOW ONCE AGAlN, WE KNOW THAT INlTIAL VELOClTY IS ZERO, SO OUR CHANG IN VELOClTY IS SAME AS FlNAL VELOClTY

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

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?

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

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.

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

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

So our final velocity is 60 mph.

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

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

I'm taking the final velocity, 78 m s, and subtracting from that the initial velocity, which is 0 m s, and you just get this divided by the acceleration, divided by 1 m s per second, or 1 m s 2.

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

So if I want to see how much faster have I gone

So it's going to be plus 1 2 times Vf, our final velocity (That's not the right color, let me actually do it in the right color so that you actually understand what I'm doing.)

IF OUR FlNAL VELOClTY IS POSlTIVE, YOU SQUARED, YOU STlLL GET A POSlTIVE VALUE

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

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.

Times this height, which is our final velocity minus our initial velocity (these are all vectors) (well, they're just positive telling us we're going to the right) and if we just multiply the base times the height, that would give us the area of this entire rectangle.

So that has to be your final velocity when you're getting off, of the plane, if you want to be flying.

So you have 5 meters per second, plus, 4 times 2 is 8 8, this seconds is gone so we're just left with m s. or this is the same thing as 13 m s which is going to be our final velocity.

If we know the initial velocity, acceleration, and the distance, and we want to figure out the final velocity, we could use this formula vf squared equals vi squared plus 2a times really the change in distance, so I'm going to write the change in distance, because that sometimes matters when we're dealing with direction change in distance, but so you'll sometimes just write this as distance.