All right. Hi, class. Today, we're going to be doing linear kinematics.
I'm going to do my best here to do this, but I don't have my iPad or my iPad's not particularly working right now. So we're going to just try our best to get through this lecture. Linear kinematics is really important in.
the branch of biomechanics. It basically describes motion without giving you or looking at the actual forces causing motion. It just looks at the actual motion itself, like the position of an object, the velocity of an object, and the acceleration.
Those are the three that we're going to cover a lot. We're going to do linear kinematics, meaning it is looking at a particle or object that moves in a straight or curved line. So not looking at how an object maybe moves around a point of axis like angular.
So we will get into that a little bit later. So first do a little bit of definitions. Position refers to the location of a particle or an object at a particular point in time.
The starting point for understanding what motion is. Distance is a scalar quantity representing the total path length traveled by an object. I'll just... Displacement describes the change in the position of an object from one to another, looking at the final and initial position over a given period of time. Well, not given a period, like over time.
But it actually looks at the actual direction of which it's traveling. Speed is another scalar quantity. It's basically the distance traveled, so it doesn't look at the... direction it's going, but basically distance over time.
So how fast an object moves over a specific distance. Velocity is basically similar to this, but it includes the direction because it's looking at displacement. So final minus initial over time for a particle. And acceleration is a vector quantity. It's basically seeing how the change of velocity over time indicating how quickly an object is either speeding up or slowing down or not changing at all, which would be a zero acceleration.
But we'll get into it. We are going to use the Cartesian coordinates, which is this x and y and also z. Again, because we live in a three-dimensional world, we have a z coordinate, which is kind of like this, maybe a line right here that would be considered z.
Oh, that does not look great. Sorry, I wish I had my iPad. This is going to be x.
and then this is going to be y. So we can place a particle on this board somewhere and that is going to be considered its position. We can track position a lot of different ways by digitizing different foot videos along an x and y coordinates.
This is someone kicking a ball, we're using their toe as the point that we're looking at and as you can see here we track it across this uh like i guess pathway of the toe kicking the ball but we use an x and y coordinate to do this we can also use a z because there is probably some z movement because it is a three-dimensional but it's easier to look at as an x and y coordinate and i think for majority of this class that's what we're going to be doing is looking at a two-dimensional like breaking it into just the pictures itself because in this picture it's really difficult to get the three-dimensional because You can't tell how far back she's going or if it's moving towards us. Okay, here's another example. We have a point on this racket right here being tracked. We have one on his hand and then one on the elbow and shoulder.
And as you can see here, we can see the motion of all four of these points. And they give us a different view of the motion being traveled. Obviously, you know, the arm is going to be traveling different than the actual racket.
And, you know, analyzing this can show if we're using movements that are a little bit more excessive and not needed. Another thing I want to talk about is modeling, like looking at a single point. So we're looking at this baton.
We are tracking that baton from the center of it. all the way down to the ground. And looking at it there is going to be a lot different than tracking it from this maybe... You know, see how it's kind of loop-de-loop, looping around if we were tracking it from the end of it. So again, like choosing the point of an object is going to give us a different view of it and the motion it's going.
So here's another example of that with a human. You know, if we were tracking his position, looking at his head, we would get a lot different view than what we're tracking from the center mass or center of his body. which is kind of just giving us a more total motion path.
Both are good. Like, you know, if you want to look at multiple different limbs and how their motion goes, that's important too. But it is easier and effective to just follow one point that doesn't like spin or rotate.
So we don't have to consider angular components of it. We... So again, we're looking at motion.
We have vectors and scalars. Now I just want to get into this. First is displacement.
So again, position is the location of a particle in space or on an X and Y coordinate. And displacement is the change of position from final to initial. So how far did it travel?
Final minus initial. Displacement is particle final minus particle initial. Well, distance is the actual total length covered over a specific specified period of time doesn't matter how long but um these are different uh this is looking at like you know the final and initial which is like so say if we're looking at a hand here how far did it travel during this throw from a to b you just track right here and we can turn this into a sine cosine tangent triangle here as you can kind of see you have an x component y component And then we have a resultant, which would be our hypotenuse right here. So that's our C for doing A squared plus B squared plus C squared.
Or, again, we can use distance formula, which is also a good way of being able to find the distance between the displacement from particle Y and final position of particle and initial period of the particle. So again, this is just covering the distance. We're just trying to see how far it goes in a vector quantity.
You can also look at the angle of which it's traveling as well. But again, we do this by subtracting the final minus the initial here. Distance, on the other hand, is looking at the total length.
How far did this person travel? And you can see it's kind of snaking its way up. That's a great line.
So that's going to be our distance. It's a lot longer, you know, because if we're just looking at displacement, it's just this initial right here all the way to this final right here. It's not even considering all this winding it goes on. It just cares about how far it went from A to B in that direction that's going from A to B. The units are always going to be in meters, typically.
I mean, we can use feet, miles, but in this class, we're going to be considering meters. So again, there's the displacement right there. Okay, so again, distance is not considering pathway or is considering the pathway.
Displacement does not. It's just how far did it go from A to B in a specific direction. Okay.
Now we're going to go into a little bit of the biomechanics and gait. We can look at the, say we're tracking body position changes using some type of tracker. We can look at that through a running gait.
So this is looking at the position of center of gravity throughout a gait cycle. So going in the anterior-posterior direction, we see throughout a one. gate cycle he's moving forward he's going outward um in the vertical direction we can kind of see they're bouncing up and down because again think about running if you're looking at your center of gravity you're going to go up and then down up and then down as you're going through a gate cycle um you can also look at other aspects but again remember there is a vertical component and a there's multiple different ways we can track motion because it's not just a straight line it's typically up, down, side, side, and forward and backward.
Okay, that's kind of all I want to talk about with displacement. We're not going to really use distance, so make sure you guys understand displacement very well and the difference between distance and displacement. Okay, next thing I want to talk about is velocity.
Velocity is defined as the rate of change of a particle from final, so basically final minus initial. It's also giving a directional component. It means it is a vector. Because we're using displacement.
Displacement is a directional component. How far did the person move in a specific direction or the object move in a specific direction? We have a couple different things here. We have average velocity.
Average velocity is like the overall length of like, say we're doing a 50 meter race. How long did it take him to get from, or like what was the speed he ran from the start to the finish? So.
basically it's a 50 meter race you ran in 10 seconds it's going to be a velocity of five meters per second pretty simple but again we know that if someone's sprinting typically they're not going to be running five meters per second the entire way through so we can use instantaneous velocity to kind of look at a snippet of a race or a of like that 50 meter run so like how you fast was he running at the 30 meter mark? So we just take a small portion of distance of maybe like 30 to 32 or 30 to 35. How fast was he running in that little interval of that 50 meter race? So he would do like between 30 and 35 point, that's a five meter distance. Maybe he did that five meter distance in, I don't know, one or two seconds. So his velocity at that exact point.
point is 2.5 that would be kind of probably not exactly right but again it's right for this example but again like someone doesn't if he's running at five meters per second probably wouldn't slow down at a 30 meter mark he's probably still accelerating um which we'll get into acceleration in a second but um yeah so that's instantaneous velocity uh speed is looking at distance over time if you remember distance doesn't have a directional component it just considers how far did the person travel meaning speed is scalar, doesn't have a directional component. Units, we're going to be using meters per second right here. Feet per second, miles per hour, those are all units of velocity or speed, but we're going to be using meters per second.
Here's a little bit of an example comparing speed versus velocity. So this person right here broke the 100-meter world record for 9.79. This is before.
Usain Bolt, I'm guessing, the Athens Olympics. So that was 2000, maybe 2004, 2000. I kind of forgot. I was way too young for that. Again, so he was, the average, you know, velocity he was traveling at was 100 meters divided by 9.79.
So it's pretty fast. But again, the speed would be something different. Because if you look at his path, he didn't take a straight path. He actually took a longer distance. So this 100 meters might actually be like maybe 110. So if you think about it, 110 divided by 9.79 seconds would show that his average speed was a lot faster than his average velocity.
But that is the case typically. So usually, not usually, our speed is almost always, if not equal to, if it's a perfect line, faster than velocity. Because we have more distance traveled. Just looking from A to B. Okay, cool.
Here's a little example. Why is 100 meter per hour fastball more difficult to hit than 80 meter per hour fastball? It's pretty self-explanatory.
The faster the ball is pitched, the less time the batter has to react to it, obviously, because it's going faster. It's getting to the plate a lot quicker. We can kind of break this down into another example problem here.
A pitcher is pitching, let's just skip to here, he's pitching from a total distance of 58 feet away. So it's 58 feet from the initial pitch to get to the plate. First thing we're going to do is convert those things we just had, mile per hour, into feet per second because we're not using metric system. Obviously metric system is way better, it's an easier conversion. It's 146.6 feet per second, 80 feet or 180 miles per hour is 117 feet per second.
And then we know how far. plate is. So now we just need to figure out what the time is. And to do this, it's going to use a little bit of algebra to kind of get, um, to figure this out. Cause we know velocity is displacement over time.
So we know the overall displacement is going to be 58 feet. Cause that's how far the ball is going to get to the plate. Um, over time, we don't know the time.
We don't know how fast it's going, but we do know is the velocity. So What we can just do here is do a little bit of algebra magic here. So what we did here is we isolated the time by multiplying this side by time and dividing this side by the velocity.
So divide here, multiply here, and that gave us this. Hopefully you guys covered some algebra. If you guys are still struggling on using this basic algebra stuff, please let me know.
I might post a video just to help you guys out. Anyway, and so then when we do that, we just do a couple of plug and chug into our calculator. We see that the time is 0.395 seconds.
That's how fast that ball from the pitcher's glove or pitcher's hand is going to get to the catcher's glove. That's how much time the batter has to react. Not a lot of time.
We look at the 80 mile per hour fastball. It's going to take a full 0.1 seconds more reaction time. I know that doesn't seem like a lot, but when you get into the majors, like every 0.00 second is going to count. That's why there's a lot of pitchers that can MLB.
They're pitching a hundred mile per hour fastball as well. Not that many make it to the MLB pitching 80. So, okay. This is another look at instantaneous versus average velocity.
So B is looking at time 0.4 to time 0.6. while A is looking at time point four, time point five, this would be more instantaneous because it's a smaller little time point, while this would be more average. It's not the full average. You can still consider this maybe instantaneous if you're looking at from three to eight, I guess. But just know that the smaller the time we're looking at for a velocity of an overall distance covered, the more we're going to consider that as instantaneous.
Okay. Velocity is the slope of displacement over time grip. So if we're tracking displacement, so x position, so it's traveling from 2 to, let's call that 8. No, call it 9. Sorry. So traveling all the way up, that is 8, a rise of 8 meters. And then the time is going to be another 8 seconds, so he is going 1 meter per second.
So again, if we see a slope in this displacement curve, displacement over time, we are going to consider that object having a velocity of something greater than 0. If this displacement was flat, this displacement was flat, we would say he had no velocity. He's not traveling anywhere. The displacement stays at 2. It goes from 2 to 2. No movement. Zero velocity.
Then we can look at this kind of graph right here. This is like vertical position over time. So if we look at segment A here, this is going to have a positive velocity. Because again, remember, velocity, let's say that's maybe 3. Time is going to be 1 second.
That's going to be 3 meters per second. A shows that he is moving at a pretty quick time. B shows a positive velocity because it's still going upward, but he is going a lot slower, a lot slower velocity because the slope is lower. He's traveling from point A to B on the vertical axis, which is how far he's going.
It's not much. Not much traveled. And the overall time is a lot longer than the segment A, as you can see here.
going there's a lot more x a lot more x going on there a lot more time passing so it's a slower velocity still positive but slower lower magnitude now we get to c c we have a big drop down over a very short period of time i know that's not a great example but very short period of time so he is having a velocity it's a negative you velocity he's going towards the direction we started and it's all relative so again like negative velocity doesn't mean he's like slowing down or anything it just means that he's traveling in the opposite direction than what we were starting from. We're traveling towards the initial direction top, which is like this is the starting point. He's traveling back towards that. So again, he's not slowing down. He's actually going really fast.
This is actually faster than point A, but it's just in the opposite direction. That's why it's negative velocity. D shows no change in displacement. So zero, zero velocity. E shows a huge spike, which is a really big...
magnitude of positive velocity because it's like not not much time is passed and then f again is showing a negative velocity it's going back towards the direction we started in okay this is another little example of this um number one we have a constant same zero velocity number two shows we're starting from here going up it's going to have an increase displacement positive direction meaning positive velocity but again Kind of going through all those. One, two, three, one are all, well, zero. One's going to be zero.
It's not moving anywhere. Two, it's going to be going up. It's going to be up.
Starting is going to, or the ending is going to be higher than the starting, so it's going to have a positive. And then three is going down, so it's going to have a negative velocity. And you can do the same thing for five, four, and six.
Okay. Average versus instantaneous velocity. So, again, like.
Looking at this position, we're seeing kind of this curve almost in velocity. So we're seeing it go up, but at a kind of a curved rate. If we're seeing that, it actually means we're seeing a curve in displacement over time graph.
It actually means acceleration. He's actually increasing in velocity as we see over that period of time. But we're going to get into that in just a second. But we're looking at instantaneous. So A. It's more of the average from time point one to starting time point two.
So this is the average, while B is more of an instantaneous one because we're looking at two time points within the average. Again, it's all just relative. Average is typically if we're looking at the entirety of a segment. Instantaneous is if we're looking at a smaller portion of the segment. Here is a velocity example.
I don't know where it is. Okay, 200 meter. uh they're from simon team well okay fact 9.4 o'clock 12 meters per second let's see if i recorded okay um so this is showing the same person who ran 100 meters and the 200 meters he ran 100 meters in 9.84 seconds which is clocking him in as 12 meters per second This is the fastest recorded ever in 1994. This is before Usain Bolt, obviously, who became the fastest because he had the fastest average speed in that race.
On the 200 meter, he also had a really fast time, but his average speed was 10.3435. So what we can draw from this, if he was maintaining speed in this 100 meters, he would have a lot faster average speed. But because different factors, maybe, you know... He ran out of steam, ran out of gas.
He actually had a slower average speed. That's kind of all I wanted to get across there. Another example here is in this 1,500-meter race.
We're kind of breaking this down. He had an average speed of 7.15 meters per second throughout the entire 1,500-meter race. If you guys don't know, 1,500 meters is a little under a mile.
Um, so we can say, oh yeah, so he ran, he was running at this average speed the entire way, but likely that's not the case. We can break it down into different segments, looking at instantaneous velocity. So, you know, between a segment within an average race, um, say this zero to 500 meters. So the first portion of his race was running at a speed of 7.13.
So it's a little bit slower than the average, um, than 50 to a thousand kind of like, you know, a lot. in towards the middle and latter half 6.96 meters per second so he's actually slowing down here and then he closed in an average speed or a speed from 1000 to 1500 the average speed between those time points or that instantaneous velocity we're looking at was 7.34 meters per second so again like we can look look at this and say oh maybe he needs to focus on the beginning or the center the middle portion of his race that's where he had the slowest um time so that's kind of like breaking this down we can kind of look at different aspects of someone's race um Another velocity example, Donald Daly's official splits from the 150 meter race at the Skydome in Toronto. Never been there.
So we see he split one from zero. So it took him 0.171 seconds to actually start his race. So that right here, that's reaction time.
That was his reaction time. So he lost 0.171 seconds. Then between zero and 50 meters, you see 5.74. We subtract this number from there because we see kind of what his speed was for the first 50 meters. Then we can subtract, you know, the time it took from 50 meters to 100 meters.
So 10.24 minus 5.74, that's the time that it took from 0.50 meters to 100 meters. And then it was 50 meters, so you do whatever that time is over 50. or under 50, so 50 divided by that time, or figure that velocity, and then you do the same thing for 150 meter mark. So we can kind of look at the average speed throughout this race, and if you look at here, the 50, as the math is already done for us, between zero and 50, he had an average speed of 8.98 meters per second, while as you look at the 150 meter, the total average speed, it was 10.12.
So he's speeding up. Okay, and then we can look at directional component. Velocity is in the direction of displacement always.
So whatever the object is moving, velocity is moving in the same plane because we're kind of tracking it in the same direction. So again, velocity has a direction. So if the displacement is going this way, the velocity is going to follow it and go the same direction. That's why we can kind of look at, like, say, this hand throwing a ball.
We can see as he gets closer to releasing the ball, vector of magnitude gets higher we can see this green line get bigger and bigger because he's accelerating he's getting a higher velocity to right when he's about to release the ball and when technically when he releases the ball that should be his fastest velocity that's how he's going to get the most out of the ball and then you see uh when he releases it he slows down kind of recovering so um we can analyze the velocity throughout a movement in order to understand like oh if he was slowing down here like he had more speed here than here means he's probably not following through he's kind of stopping before he even releases the ball so another way to look at that velocity graphically speaking so again we can see the direction of the slope that will show the velocity is either positive or negative so if this is position from this point to here it's going to be positive velocity we're going to go back backwards a little bit, so that's going to be a negative velocity, and then we'll go all the way up here, another positive velocity. So when we differentiate a displacement and time graph, we obtain a velocity over time. This position helps us when we graph it like velocity over time, this helps us understand how velocity changes over time, and this is going to lead us into our next segment of acceleration, but you know, change of velocity over time. time is acceleration.
So whenever we see that change, but so points where the slope of a tangent line to the displacement time are equal to zero. So tangent slope equals zero. This is identifying where the slope of Mika, sorry, my dog is whining.
Hey, stop that. Come on up here. You can say hi to Mika.
She is being a little needy right now. Go on. go lay down lay down um okay so tangent slope zero where was i at um these are critical points because these correspond to the velocity of time inflection point looks for inflection so inflection point looks for an inflection point on displacement time curve is where the curves concave changes these points uh correspond with a maximum or minimum velocity on a time graph um we see a sharper curve than anything else i'm just going to show you examples here um we're tracking this velocity so see how the position is going up here hi why are you whining why are you whining here give me one sec i'm gonna go uh sorry about that my dog needed to go out she was definitely whining for that um anyway so Again, we can kind of break this position into different segments here.
You have like segment one, segment two, segment three, segment four. And then we can graph the velocity based on that. And you can kind of see here, we see a positive velocity for segment one. But as it gets kind of closer to this point two, we start to see it go down. So again, like anything up here.
means it's moving in a positive direction. It has a positive velocity. It's going forward.
But then, you know, as we get to here, we start to go backwards, meaning that velocity is going to be negative. We're still moving, but it's going in the backwards direction because it's going towards where we started. Then we get to segment three.
It's going to be going upward, meaning it's going forward. And then again, segment four is going to be negative so that's how we kind of graph we can graph this velocity according to the position and here's just another example to really hammer it in usain bolt's 2008 world record run he actually broke that world record um i think 2009 i think i think it was 2009 i think i have a slide of that up here somewhere but um we can look at his velocity all the way throughout the race and all these 10 meter time segments so for the first 10 meters we saw 7.39 from zero to um start so again remember 0.164 that's when he started his race is when he started moving after the gun went off that is basically reaction time that we're looking at there um pretty good reaction time um then we see 7.39 is his velocity from zero to 10 uh from 20 10 to 20 we see it go up 10.36 we see it continually go up and up and up until we get to this almost like constant speed and that's what why we have elite runners is because they can get to a high velocity and keep that all the way through and if you kind of look here at the end of his race it's actually going down like it was a slower velocity he's decelerating a bit and the reason being is during this race he was looking around he was looking at the people behind him which You never do in these types of races. You're supposed to keep going forward. And again, we can see this here again in this other race. We see that his fastest time segment is at 70 meters.
And again, he started slowing down a bit at the end because, again, he just kind of cruises once he has a big enough gap. OK, here's a little question. When running a loop on a track and the initial and final positions are on the same spot, which of these is true?
Well, distance is actually greater than displacement. So technically, if we're ending and starting on the same spot, the average displacement is zero. So if we're running on a loop, well, that's a really bad loop.
And this is the starting position. You go all the way up, over, and around. You start end here.
You didn't go anywhere. So your displacement is zero. Kind of interesting, huh?
Here's just something, you know, we use a radar gun in order to look at speed. I'm not going to go into the phenomenon here, but it's the Doppler effect. We actually send wavelengths out and we can get them back at different wavelengths because they'll bounce off of it.
And that's how we can kind of change in those wavelengths from start to finish is how we see speed using a radar gun. OK, how do we measure average speed in a lab environment? Well, we collect a lot of data looking at someone moving. We can look at different markers and see basically how they move and how quickly they move, given a different task.
So if we're looking at average running or walking speed, we can use these markers in order to do it. I don't worry about that. I'm not going to be on the test, like how we do it.
Acceleration. This is a long one. Acceleration is the rate of change. of velocity of a particle. So we are seeing a change in the vector quantity of velocity, meaning this is also a vector quantity.
So it has magnitude and direction. And basically it's just seeing the final velocity minus the initial velocity over a given period of time. So we're looking at average velocity of like a race. How quickly did he go? If he started at zero, he went to 10 meters in 10 seconds.
10 meters per second in 10 seconds, it's going to have an average velocity of 10 meters per second squared. Um, reason being is when we're looking at the units. So velocity is going to be 10. This is not, there we go.
10 meters. And why is that not tracking that? That does not look good.
Second, we divide it by say. 10 seconds. These seconds are going to square. The meters are going to stay the same.
So it's going to be one meter per second. And because we have two getting divided by themselves, it's actually going to square that square. So that is your unit of measurement for acceleration.
Oh man, that does not look good, but it's right here. So sorry. Yeah.
10 meters per second squared. So again, the units of acceleration equals meters per second squared or feet per second squared, but we're using meters per second squared almost always. And average versus instantaneous is similar.
So average is like looking at the overall race from like, if it's a 50 meter race, the entire 50 meters. We're just looking at the average velocity, but if we, or average acceleration. But if we want to look more instantaneously, we'll look at like a snippet of velocity change throughout that. to see maybe how much he's accelerating at the beginning of the race versus the end of the race.
So instantaneous, again, is just like an instant within an average race or average time period. I usually like using races because it's easy to understand. So acceleration, again, is a measure of change in velocity. If we're looking at someone doing a jump, like a jump kick here, we're looking at the velocity.
It's changing from going forward. starting to go upward, and then all of a sudden he's like off the ground. So we see a change in overall magnitude of velocity, but we also see a change in direction.
So any change in direction or magnitude of a velocity is going to be due to acceleration. So as we can see here, we went from initial going this direction to final going up. and all slightly backwards meaning he's still going forward the velocity is going forward but the acceleration is actually going almost backwards and upward and you can kind of get it through doing this tip to tail method a bit in order to track that this change in velocity is basically the final minus initial and if the initial velocity is going kind of like this way It's a little bit confusing, but as we kind of go through these examples, it is due to change in magnitude of velocity and also change of direction of velocity. So in this example of the person jumping and you can see how their velocity increases and changes direction as they push upwards, the acceleration vectors depicted kind of below it are also changing.
So it's important to note that these acceleration vectors are not. usually aligned with the actual direction of displacement. They're kind of going in different directions.
Not always. Like if you're seeing someone accelerate in a race, like sprinting, where you see the acceleration kind of go in this side of, you know, wherever the displacement is going. But, you know, it doesn't always mean that.
It just means which way is velocity changing. So again, if velocity is going slightly upward from a starting position, that's going to be a backward when you kind of look at the actual change of it. So when the person is in the air, the situation kind of, to try to simplify it, the acceleration vector is always going to be directed downward because gravity is acting on them. So when this person gets off the ground, now they're accelerating downward. Because think about it, when you jump up, what's acting on you?
What's happening? You're decelerating as you go up. So you have gravity acting on you.
Unless you have jetpack on you, then you'll accelerate upward. But you're always going to slowly, slowly stop going up. or else you're just going to keep flying off.
So your acceleration is going to be downward, and that is due to gravity. So when you're in the air, when you're considered a projectile, gravity is always going to be the force pulling you down. Other than that, it's kind of your body generating different accelerated forces in order to get you up and off the ground.
Tangent to velocity time curve. So the acceleration vector can also be understood as the tangent to the time. velocity time curve at any given point.
So this kind of helps us visualize how acceleration affects velocity. over time. So like the change in velocity, you kind of create that into a triangle, kind of like we did here, it is going to be this right there.
Okay. So question is a 400 meter runner that is running at a constant speed around the track accelerating? Kind of a trick question, but yes, because they are changing in direction.
It doesn't. always have to be change in magnitude it can also be a change in direction because again you have to when you're turning on a track you're changing your direction you're actually accelerating maybe more towards the left when you're going around that turn okay um now let's look at this velocity over time versus acceleration over time so if The signs of velocity and acceleration are the same. We see speed increasing.
If the signs of velocity and acceleration are different, we see speed decreasing. So what that means is a person could still be moving forward, like have a positive velocity. But if that velocity is changing maybe downward, or even like plateauing, it's not going as a slope. we're going to see acceleration change.
Because again, we're going to see, or if he's going constant speed, we're going to see zero acceleration. But if we see him sloping in one direction or the other, he's speeding up or slowing down, we're going to see a positive or negative acceleration. Again, negative acceleration doesn't mean that they're stopping or slowing, or stopping completely or going backwards. It just means that their velocity is getting slower. You can kind of see this a little bit better looking at this velocity.
over time graph. So we see the star here. They have a starting velocity of 1.35. To this point right here, where they're going down maybe a 1.3, that is a negative acceleration.
He is decelerating. We can kind of draw this graph out a little bit. So when we look at different time points, we can draw these all the way up here. So from point here to here. He's still going in a direction.
He has a positive velocity, but he's decelerating. So we're going to have a negative acceleration. Then when he starts to get faster, he goes from like 1.3 to 1.5, you see a positive acceleration. Then he gets slower and slower and slower, which means he's decelerating throughout this time period. Shows that, you know, he's in negative acceleration.
Doesn't mean he's... Once we get to like a plateau... So say we continue this graph out a little bit further. Say he goes like this.
He maybe consists constantly swimming at a speed of 1.5. That means he has an acceleration of zero. A constant speed means zero acceleration.
Then we kind of look at this graph here. So we had the time, we had the distance, and we have now the velocity and acceleration. So when we're looking at velocity from zero to 7.35, We see he's accelerating 3.83.
So he's going from a zero velocity to 7.39 velocity. Means that change over, you know, whatever time, this is like maybe like 1.7 seconds. We see that change, the 3.83 meters per second squared.
And then as the race progresses, we see the acceleration go down. Why? Because he's getting closer and closer to top speed.
You can't just keep accelerating. You can't have an increasing number of acceleration. If it keeps going up and up and up and up, you just continually is gaining more and more and more speed at more drastic feats.
It's just not sustainable. We see it with like, you know, like rockets and stuff like that where you increase acceleration as you go up. But typically, you see the initial, like...
increase in boost and speed be the highest acceleration when he's taking off from the blocks especially in a good race you want to see the highest acceleration at the beginning so you're getting to your top speed faster and then as he goes to the race you kind of slope off you have 0.13 acceleration so you kind of like almost stopping accelerating then we get down to the end here he is starting to decelerate a bit because we're seeing his velocity go down over time so again you can see that again with this graph you Yeah, so those are the big components of acceleration that I wanted to talk about. We can analyze spatial and temporal kinematics variables to understand different gait patterns. We can look at kinematic data on different axes.
So we have a Z, Y, X, and we're in a three-dimensional state. So we can look at how someone's moving throughout a gate pattern kind of by breaking it down into kinematic components of their gate. So just as far as timing components goes, relative timing components, during a walk, we see struts.
like a stride, you know, we have stance phase be equal to 60% of the phase. So if you're walking, if it takes you three seconds to do a full gate walk, 60% of that three seconds is going to be during in the stance phase where you have a foot on the ground, your whatever feet, foot you're looking at on the ground, or like even double like, you know, stance phase and then what we have 40 is going to be a swing phase where that foot is actually moving so and that's going to be you know 40 so uh thing i want to get across here is like all these movements encompass in a single step can be divided into phases that almost everyone should kind of adhere to so like 60 of your walking should be in stance phase 40 should be in walking phase if you want to oh we need to skip you there if you want to you know have good gait and if we see anything kind of stray away from that we can maybe identify some issues maybe the person has parkinson's and they spend more time in a stance phase where they're you know a little bit safer or even like when you get older and you see people start to shuffle they're increasing that percent of their like their gait cycle in a stance phase you know when someone's shuffling you're kind of always having a foot on the ground. You're not really moving that much. So if we move away from the swing phase, having 40% to having maybe 30%, because say maybe there's a problem with that person's gait. So it's a way of analyzing their gait by using kinematic data timing components.
So which factors can determine how fast someone can walk? Well, we have two different factors. We have stride length and stride frequency. So how far or how long of a step and then how fast it goes from step to step to step so how long it's going to take you to get from one step to the next step so again if you have longer steps longer strides and a faster stride frequency quicker like you know faster stride rates you're gonna have faster walking speed faster gait it's just kind of like easy to think so gait speed is equal to um you know let's see whoa you There we go. Gate speed is equal to stride length times stride frequency, which makes sense.
How fast are you walking and how long are your steps? How much distance is being covered? Okay. If the heel strike of one limb to the heel strike of the contralateral limb, we can look at the different aspects on average versus instantaneous. Like kind of.
We can look at the average step length and step frequency, or we can kind of take different components of it to get more of an instantaneous. I kind of like this graph a little bit better. So support and double support during walking phase.
So the gait cycle is broken down into a lot of different things. We can further break it down from just stance and swing to more support versus non-support. double support, right swing, left swing. And again, they should kind of have similar components to them.
So understanding the distribution of time between the support and the swing phase is crucial for analyzing different gates, different types of gate, different problems with gate, whether it be in walking or running. Because these phases impact stability, propulsion, and overall efficiency. So again, if we see changes... In these timing things, so like, for instance, in running, the support phase will go down, might reduce all the way down to as little as 40%, which makes sense because we know we're not, we have a time in the air where we're not even, you know, touching the ground.
So again, that's kind of makes sense that we see like, you know, if we go from one type of gait, like walking to running or sprinting. we will see this dance phase go down and that's kind of how we can look at that. as well. Okay, here is a question. So during normal speed walking, how much time is spent during the support phase?
60%. If we're looking at one gait to another, even if you're going as fast as possible, walking still keeps the same consistent gait patterns, 60%. It's not going up, it's not going down.
When we start to see changes to this, that means we're going from walking to jogging. So when we see that support phase go to maybe down to 40%, we know we're no longer doing a walk. It's going to be a jog or a run or sprint or whatever it is.
This is a lot here in this figure. We can kind of look at the speed of different gates. We have walking, running, and sprinting. Obviously, the from walking to sprinting sprinting is gonna be the fastest meters per second and speed uh we also see stride length go up as we go from walking to sprinting which makes sense like you see people's strides really lengthen out because you want to cover as much distance as possible on each stride um uh we see stride rate um go up as well you're increasing how many strides um again stance versus swing if you look at the sprint it's 25 of your time is spent in stance and 75 is spent in swing again when you consider like you're kind of like propelling yourself forward almost like jumping each stride makes sense you're not going to be much in that stance speed you're going to spend a lot more time in the swing phase well again if you look over here at the stance phase versus swing phase of walking it's relatively 60 to 40. um Normative values.
What is the stride frequency when a man is walking at 1.3 versus 1.4? So as we can kind of see here, in men and women, we see men have a higher speed than women on average when we're looking at gait, like maybe jogging or running or whatever it is, which makes sense. Men typically...
tend to be faster than women. The question is why? Why do we see that?
Well, the big reason here is we have C stride length on average is larger in men than women. So they're just taking larger steps, larger strides. While we see even the cadence is actually faster in women, which is interesting because cadence is the other factor in speed. So it's not just one thing over the other that controls speed. There's other factors.
And we see actually women have a... overall average cadence that's faster than men. What this can be due to is actually having smaller strides. They're smaller strides, less ground travel across, so you can actually see the speed increase or see the cadence increase.
Here is kind of looking at the transition from walking to running where we get that zero double support time. That is the flight phase where basically you don't have either foot on the ground. And that's kind of like the big thing when we look at these gait graphs here, when we're kind of looking at the time components of each time spent in a different phase. Walking, we see that stance phase and even a double support phase.
When we get to running or jogging, we don't see a double support phase. You don't see both feet on the ground at the same time. that you're just walking at that point.
The big component is you have a flight phase. That's what defines walking to jogging or walking to running, the differences at least. A couple more slides here.
Guys, I'll try to get through these really quick. So we have stride length and frequency. So if you're trying to increase speed, we can do two things.
We increase stride length and we can increase stride rate. But as we can see here, as we increase speed, stride length kind of plateaus out at a specific point, and we see stride rate be the one that kind of takes over. So again, we can increase both in order to increase speed, but we see stride length only increase to a specific point, and then it plateaus out, while stride rate kind of takes over to continue to increase speed. Okay. Again, gate speed is stride length times stride frequency.
And we see here as speed increases both will increase but stride length will plateau out while stride rate will continue to increase as we increase speed. I don't need to go over this. There's a lot of applicability of this. Okay, so during normal speed walking, how much time is spent during single support?
We kind of talked about this a little bit earlier. It's 40%. If we knew the stance phase is always going to be 60%, 40% is going to be for the other portion.
So again, just because we increase the speed of gait walking, it does not mean we change the relative. percent time spent in each of these phases. So okay, a little under an hour. Sorry this video is so long. If you guys have any questions with this, you can either talk to me or your lab assistants.
A lot of what we're going to be covering is going to be the acceleration stuff, acceleration velocity and displacement. So really I recommend focusing on that relative to the gait. But all right, I will finish.