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Zainab S.

July 14, 2021

So for position do we account for + and - signs?

Cielo Ace C.

August 29, 2021

+ position = going to the left

While - (negative position) = going to the right. Consider the cartesian plate.

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

04:27

Kai Chen

(I) A 110-kg tackler moving at 2.5 ms meets head-on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after the collision?

01:24

Keshav Singh

(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

03:04

(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?

04:15

Kathleen Tatem

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welcome to our one dimensional Kinnah Matics videos, where we will consider position and displacement, I should say not just position in displacement, but also position displacement in distance. So these air three important terms that I mentioned in the introductory video and I talked to briefly about what they mean. So let's dig into them a little more again. We're gonna be looking at this straight line where we've defined the next equals zero, and then we've got some way of breaking up the distance as we move away from zero. Let's go and just say that we're at X equals 0 m and then we have 1 m, 2 m, 3 m negative 1 m negative, 2 m negative, 3 m and so forth. So when we start thinking about position, it is literally whatever grid system we have laid down. Whatever coordinate system we've laid down on top of the world we're considering position is just the absolute number that you happen to be standing there, or that the person or object we're considering happens to be sitting at. So, generally speaking, we're going to write position as X. It's probably going to vary as a function of time here. No. It's important to recognize here in one dimensional mathematics that we might be to the right of X equals zero. We might be to the left of X equals zero. And because it matters which direction we're and we're actually going to consider position to be a vector, that means that not only are we looking at an absolute number here a scaler number, but we also have some direction associated with it. So whenever I have a variable and I draw this arrow, um, sometimes I'll use a full arrow. Sometimes I'll use kind of a half arrow thing just because it lets me drop closer to the variable then and keep track of things Whenever I draw this, it means that the quantity I'm looking at is a variable. So this is our position. Variable is X. Now, when we change position, as I mentioned before, say we go from X equals zero to X equals three. What we're gonna have is a displacement. So we're gonna know denote displacement with this delta X quantity here now Delta X, what it is is saying a change Delta, the Greek letter Delta always is going to denote a change for us. So we're going to say Okay, I've had some change in X. That means I have an ex final minus an ex initial or X nut, as we often right in physics. So we have an X final minus and ex initial. So it's a change in X, and because we're subtracting two vectors from each other, it means that we also will end up with a vector here. And so this is what we're going to call displacement notice. This means things like if we start and end at the same place than our total displacement is zero. So if we go out and back, we have zero displacement. Or similarly, if we happen to go, run around in a circle for a while and like if you're on a track or something and you run around and stop at the same place, your displacement, your total displacement was zero. Now, if we're talking about total distance, that's a different ball game. What the total distance says is, I am interested in how far we traveled, so I'm going to use the variable de here, and it's how far you traveled. We'll call this total distance. So, for example, if you're on a track and you run 400 m around, which is one loop around the track, then the total distance would be 400 m. Meanwhile, your total displacement would be zero and you're changing in your position. You would have started at zero and ended at zero, but you would have had many different positions in between. So those are the important differences between all these things. Notice all of them are going to be measured in meters because positions and meters displacements just a change in position. So that will also be in meters and then distance were pretty accustomed to using things like meters or miles and inches or kilometers, or depending on what country you're from now. Um, I mentioned this word before vectors, which is a very important word in all of the future videos in physics. And now we've talked about this absolute position idea where we say, Oh, we're at 0123 or 0 m, 1 m, 2 m, 3 m. But when we talk about a vector, we have to talk about what is our direction? So a vector involves both the magnitude. So in this case, something like 2 m and a direction now directions a little, a little overlooked sometimes in one deacon O Matics. But what? The direction is literally dictated by whether or not you have a positive or a negative in front of your magnitude, and that's it. Now, as we go on and we talk about vectors in more complex fashion, we'll use some more complex notation to deal with it. But generally speaking here with way that we would denote a vector is you would say, Oh, well, I'm at the position X is equal to 2 m and the positive and negative erection will say we're at positive 2 m here and then I could put behind this something called X hat. Okay, where X hat is actually the vector part here. So 2 m would be the magnitude ex hat is the direction, and what we're seeing is that X hat says we're moving in the X direction as opposed to the Y direction. Up and down or some other direction is the direction. And the hat means that this is a vector that has a magnitude of one. So we're literally taking some magnitude a coefficient and then multiplying it by a vector that has a magnitude of one. This is called a unit vector, and this will be more important once we start considering mawr dimensions than just one dimension. Um, but for now, it's good to get in the practice of writing this X hat now, because we're in a calculus space physics course, you probably won't see X hat so often, except maybe in the very at the very beginning of your course. Generally speaking, you're teachers aren't going to use X hat they're going to replace it with I had. Okay, so this is an eye with a hat on top of it, Similar to how we had it x with a hat on top of it. Uh, this is really due to engineers more than anything else because they tend to use I, j and K often because X, y and Z air used for variable names. So they use I, J and K instead to represent their unit vectors. And we follow suit in physics. So rather than having X hat, will use I hat, which means the X direction just like what expat means and it is also a unit vector, just like X hat. So if you're if you're not sure what all that means, just just stick with it will continue to use this notation. It will, your understanding will grow and it won't be a big deal. And if you continue to follow this as we go through the one Deacon O Matics, when we get to the two dimensional stuff, it will make a lot more sense. Alright, I continue. I encourage you to continue watching the videos. We're gonna talk about position displacement in distance and the next in the following examples. And then we'll move on to talking about speed and velocity.

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Work

Kinetic Energy

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