1D Motion & Kinematics - Physics 101 / AP Physics 1 Review with Dianna Cowern

meters per second squared. However, we'll see how fast it really accelerated when we get to that issue. We can use these shapes to find an equation for the distance traveled. Here's something fun. I'm going to do my third favorite trick. I'm going to replace something. Look at these two equations that I wrote: the area of ​​this triangle, 1/2 times delta v, and then this right here is just a simple definition of acceleration. Note that both equations have a delta v. I'm going to rewrite this by doing exactly what I did before mentioning delta t. These cancel out and I see that delta v is just acceleration multiplied by time.

It's a simple little algebraic substitution. When I see that two different equations have something in common, maybe I can combine them. And if I plug this in here, I get something really interesting. I understand that the area of ​​the triangle, this here, because of my acceleration is now 1/2. Bring it up: 1/2 times delta v, at, and then another t, at squared. Now I'm going to put all this together. I'm going to put together the area of ​​my rectangle and the area of ​​my triangle. That's 1/2 squared plus... where's the other one? V not you. And in this problem, what were we doing?

We were doing the position change, which has two pieces. It has how far I would have gone if I wasn't accelerating and how far I went because I accelerated. And remember, I don't need both. Maybe I have a case where I'm not accelerating and this term is over. Maybe I have a case where I had zero initial velocity and this term disappears. You could have a case where you are doing both. You could have a case where you have an initial velocity and you are accelerating. And then I need both. Now let's rewrite this, but we're missing a key term: starting position.

My starting position here was zero, so I didn't need it. But if I add it to these two terms, I get that the position is equal to the initial position plus the initial velocity times the time plus 1/2 times the acceleration times the time squared. You may have already seen this equation many times. We call this the equation of

motion

. Ahhh! Where you are is where you started plus how far you went due to your initial speed plus how far you went due to the fact that you are accelerating. I bet you never understood this equation so well.

We now have a simple master equation: the equation of

motion

. This equation is important. Write it. Tattoo it on your arm. And we just derived it. We simply look at the area under a velocity versus time graph to find the displacement, and from there we derive the equation of motion. That is very beautiful. You can use this to derive all the other equations you have in your book or cheat sheet. Here they are, in case you want to memorize them. And now I can solve my question about the ping-pong ball. How fast does the ping-pong ball go when it leaves the tube?

I only need two measurements, the distance the ball traveled, which I measured using the nice tape measure on the screen and got 2.29 meters, and the time, which I measured knowing that it was filmed at 18,000 frames per second. So each frame is 1/18,000th of a second. And I get around 0.0121 seconds. So my average speed is 2.29 meters in 0.0121 seconds of distance in time, which is equivalent to 189 meters per second. If we assume constant acceleration, my final velocity is double, so 379 meters per second, which is equivalent to over 800 miles per hour. Dude, that's faster than the speed of sound, which doesn't seem right.

So I redid the same kind of measurements, 4.5 centimeters of pipe, which only required three frames, and I got 270 meters per second, which is much more reasonable. So why the difference? Well, it's not really a constant acceleration. There are a lot of complicated things going on, including the fact that air is coming in quickly, not just pushing the ball. He's also trying hard. But I did measure an incredibly high acceleration of 47,000 meters per second squared during the first 10 centimeters. Can you think about how I did that? And voila. Now, my last question is: can you build a safer bike helmet?

Well, let's say you have a mountain biker. He wears a helmet and crashes into a tree at about 10 meters per second, about 20 miles per hour. And he loses his balance and falls off the bike. I'm a much more careful cyclist. I want to know what his face feels like. Specifically, I want to know what the acceleration of his head was. His head stops completely in the distance at which part of his helmet collapses, which we will generously say is about 10 centimeters. Now, I don't have any fancy laser devices, I just have his speed and the length of the helmet, 10 centimeters.

If I simply plug this into my equation of motion, which we'll write again, this term disappears because its initial position is simply zero. I know its initial speed. I don't know its time and I don't know its acceleration. I have two unknowns. Now, there's probably some fancy equation in your book that you can just plug in and solve, but to me, that doesn't give me any intuition as to what's really going on. So let's do this. I have this equation for x, but I have unknowns, a and t. So how can I find one of them?

Well, I know I started at 10 meters per second and stopped at zero. So my speed change is 10 meters per second. So let's assume a constant deceleration. We'll just graph it. That means you go from 10 to zero. This means I know my average speed, because it's right halfway between 10 and zero. It's five meters per second. So my average speed is five meters per second. And I know that I was at the average speed for 10 centimeters, or 0.1 meters. Then I knew how long it took me to stop. I know the time, because the speed is the change in position with respect to the change in time.

All I have to do is reorganize to make the time. This goes up here. This goes down here. X over v. I know this is 0.1 meters and 5 meters per second. And I see that the time it took me to stop is--let's go this way-- 0.05 of a second. Now, its acceleration. Well, it is the change in speed, which is 10 meters per second, compared to the change in time, which is 0.05 seconds. And I get 500 meters per second squared. That's about 50 times the acceleration you would feel from gravity here on the Earth's surface. So that's a lot. But you can survive.

You may have heard of this type of acceleration comparison called gs. So for example, my friend Destin from the Smarter Every Day channel went up on an F16 and experienced 7gs. Hoping it happens one day. The highest gs ever recorded experienced by a human being was 216 gs. Do you want to hear something crazy? The mantis shrimp punch, that's the majestic creature I made an entire Physics Girl video about, its claw accelerates up to around 15,000 gs. So now you're thinking, thank goodness she was in a bike accident and wasn't hit by a mantis shrimp. We found out that you can survive a bicycle accident, but you can still get a concussion.

So how can you make your helmet safer? Well, if you increase the distance you need to stop, say if you have an inflatable bicycle helmet that gives you another 10 centimeters, well, that's like the crumple zone, the front of a car that crumples when you get into a collision. , helps you feel less acceleration. This way you can solve the problem of the inflatable helmet. Go to Google inflatable bicycle helmets. Calculate what the deformation zone of a hull would be and calculate the acceleration. Send me the answer if you do. I believe in you. That's our first lesson on

kinematics

.

When asked what you learned today on YouTube, here are two important takeaways: If you can turn your

physics

problem into a graph or image, do it. If you can find your average velocity in problems with constant 1D acceleration, use it. And here are all the problems we did today. You know why? Because the only way to really learn

physics

is by solving problems. So here's your homework. Solve all these problems again on your own. TRUE. I'm not kidding. Go make them. You can also find many more one-dimensional motion

kinematics

problems online. So if you find other interesting problems, please post them in the comments.

We just touched on the basics of kinematics. Because if you stick with physics, stranger things happen. For example, throughout this lesson, we assume that time passes at the same rate for everyone, that one second for the cyclist is equal to one second for the tree he hit. What we just did is not fake physics, but it is a less precise approximation. If you want to be really precise, time passes more slowly if an object is moving. And you really notice it when that object travels close to the speed of light. That's real physics. You get interesting thought experiments, like when one twin leaves Earth for two weeks and comes back to find that his twin has aged 40 years.

If you continue studying physics and take a class on special relativity, you'll learn about that madness and much more. And I hope you stick with physics. And now a message for you from a special guest. Hello, my name is Simone. I run a YouTube channel named after myself because I can't think of anything funnier. But a little known fact is that she actually used to study physics in college. I dropped out after only one year, which is a bit of a hiatus, but I love physics and I'm so excited for you to learn more about it, because what better way to understand the world than through the magic of numbers. ?

Good luck.