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1. PhysicsCourseOnline: Are you interested in learning all about physics? Do you want to master the high school in AP curriculum? Whether you're a high school student or an entry level college student, this course is for you. Each syriza dresses every topic thoroughly with lessons, demonstrations, an example problems.
2. Physics - 1D Kinematics - Uniform Accelerated Motion Examples: All right, we got moose. So here, we're gonna go through some you am example problems. All right, let's go through the whole process. Ah, as clear in his concise that possibly cancel first step. Read a problem. So we have an Olympic class sprinter. Starts a race with an acceleration of 4.5 meters per second squared. What is her speed? 2.4 seconds later. First job done. Second step making knows list you could write. No one's out where you can just simply make a list. So I'm gonna go through what? I'm going to read the obvious stuff. So, you know, with an acceleration of 4.5 meters per second squared, that's her acceleration. So a is 4.5 meters per second squared. We wanted her speed 2.4 seconds later. Here's what a lot of students did. They read the number that scans cancer. I don't number and they look great before its speed. So they go ahead and write. Speed is 2.4. That's not it. What is her speed? 2.4 seconds later. This is time. Time is 2.4 seconds. What is her speed is the unknown. But before I make my unknown, you can't remember. We need three variables to find every other variable. I only have two here. There's something else I need to read. An Olympic class sprinter starts a race. Think about it. What's true about her motion in the very beginning of the race? Yeah, her initial velocity is zero. Now we want to know her speed 2.4 seconds. That's her second philosophy or her final velocity. You can write V to V. F. It doesn't matter pretty much the same thing. Also, it might help just to write down all five variables every single time. If you know it's a kid, a Matics problem. So the other one that would be left is displacement. But since we're not asking for displacement, I did not need to write this down. This last one was just totally optional just there to make sure I'm keeping track of all five. OK, so for now, I'm just gonna look at these top four. Now. What we've got to do is we gotta think about those. You am equations and think Well, what equation incorporates these four variables in it Now, normally I do not encourage you to look up your equations. I'd rather you just know them. But if you've got a resource in Fernie, go ahead. Look at it. Take a time. Look at it. You probably eventually saw VF equals V I plus E t. Now I'm writing it down the format that you probably have in your notes. But nor does I put one into here, and I did that on purpose, the first in the second speeds, not the final in initial. It's really totally okay to do one and two, but it's probably smarter to put that in your equation. So instead of the African gravy to that's the final velocity, I said, Avi, I'm gonna v one, cause that's my initial velocity plus 80. The next step is to rearrange your equation and substitute. Well, we don't need to rearrange. Fortunately for us, it's already in terms of you to, So now we've got to do is substitute. It's important to substitute in your units as well. Ah, whilst it's not mandated because we've already included units somewhere, it's helpful to go ahead and include them right in the problem. You'll see that I'll get pretty lazy early on, and I'll stop doing it as long as they've done it once. Typically, don't do it again. Um, but it can be very helpful to determine your final units. All right, go ahead and solve this on your own. I'm gonna go ahead, and I'm gonna solve it as well. Okay, if you have not had enough time to solve yet positive about to tell you the answer, Okay, The answer is 10.8 for the magnitude and my units. While I'm looking at velocity, it's a meter per second. That is my final answer. And that makes total sense. That's perfectly appropriate. All right, I will take opportunity, explain a few things here right now that I did not really explain earlier. One. If you're dealing with a high school curriculum, you likely will earn points as you go. Not just your final answer. And New York State. You get one point for properly identifying the equation for proper substitution with units and you get another point for proper answer with units. However, the substitution when units you don't have to seven with units. If you made a knowns list with units, I think it's essential to make unknowns list, and I think it's equally essential to include units. So at that point, since you've done that, subbing in with units is optional. Got it? Okay, well, let's move on. Number two. Ah, well thrown ball is caught in a well pad. Admit if the deceleration of the ball is 2.1 times 10 to the four meters for second squared and 1.85 times 10 in the negative. Three seconds elapses from the time the ball first touches the MIT until it stops. What was the initial velocity of the ball? Well, let's make her nose list. We know the ball has a deceleration. Now that implies that it's causing the object to slowed down. I'm going to treat the Ford. Initial velocity is positive as a result, on a referred to this value as negative, it's acting against my forward motion. So I say the acceleration is 2.1 times 10 to the four meters per second squared. We know that 1.5 by 10 and again three seconds elapsed. That's my time. It lapses from the time the ball first touches the mitt until it stops that's a hidden variable. Stops That's at the end. Its final velocity is zero. We want no, the initial velocity of the ball. All right, go ahead. Think of the equation to use positive. You need more time. I'm about to write it down. Yep. It's the same equation. We just did the F equals V I plus 80 my final glossy zero. So I can sub it in a zero, or I could just cross it out across it. Out. I need to isolate V I to do that. I'm going to subtract 18. I'm gonna write it in right now, but I often don't write in my math steps because I think you should be proficient enough to build. To do this on your own. The I will equal negative a t. Now I need the substitute in. It's negative. Eight times t negative is part of the equation, not part of variable. I do need to include Oh, look at that. I said it out loud, but I didn't write it down. Remember? Earlier is the deceleration is acting against. It's forward motion. Some calling this negative. I should have written that negative in. Sorry about that. my initial velocity is negative times negative A which is negative. 2.10 by 10 of the four I'm put in parentheses around it, just so we can not jumble up our negatives. And then times my time 1.85 times. 10 The negative three. Look it. Just like I said, I'm going to start getting lazy, not put my units, and that's OK, because I already did. Once over here, I wanna go to plug in my value. My negative will cancel out this negative, which makes sense. That means the ball was initially going forward and the glove was pushing against the ball to slow it down. Go ahead, pause this. You can figure out the answer on your own. All right, I'm getting an answer of 38.85 and its velocity. So my units are meters per second. Let's move on to the next problem. Three. A boy and a gun is accelerated from a firing chamber to the end of a barrel at an average rate of 6.2 by 10 in the five meters per second squared for 8.1 by to negative four seconds . What is its muzzle velocity. In case you don't know that, it's the final velocity. Make unknowns list A is 6.2 by 10 in the five meters per second squared time is 8.1 by 10 in the negative four seconds. If it's boats being excited from the gun, so what's it? Starting velocity? It must be zero right V one is indeed zero V two is what I'm looking for. Once again, same Equation V two equals V one plus 80 v 10 So therefore, V two is simply eight times T, which is that 6.2 by 10 of the five times the 8.1 by 10 to the negative four. Let's figure this out positive. All right. I got an answer of 502.2 meters per second. Cool. You know, double check. Make sure makes sense. It should, You know, accelerations. Positive object, sir, from Russell's gonna increase in speed in the positive sense. Some bullets. Let's get the careers in a pretty high speed. This is pretty legit. Let's move on. Number four will entering a freeway. A car accelerates front rest. I'm gonna go ahead and put Minoans and as they go now, So Karkh So it's from rest. That means its initial velocity zero Eddie rate of 2.4 meters per second squared for 12 seconds. We want to know a how far the car travels and be what its final velocity is. Here we go. We're gonna actually find every single one of the motion variables. Let's do our the displacement. First, we're looking for an equation that has V one in. It has time in it and it has acceleration in it. Sometimes he after used to equations. In this case, we don't We're gonna use change in displacement is equal to V I t plus 1/2 a t squared my initial velocity zero zero times. Time is room. This whole term goes away. That's often the case in this equation. That's good. Helps her math me a little bit easier. Somewhat. Displacement is simply 1/2 a T squared. That's gonna be 1/2 of my a 2.4 times my time squared. 12 squared. Don't be silly. Make sure you're only squaring the time. Please make sure you use your calculator work practice properly, as I do these examples you should do Emma's. Well, make sure you're getting the same answer that I'm getting. If you're not either un wrong, which is possible, happens all the time or you're wrong, Which is probable as well. So make sure you actually practice this. I'm gonna pause this while I figure this out. You should as well. Okay, I got an answer of 172.8. And that unit is meters because we're dealing with distance or displacement. Cool. That's answered. A Now for B. We want to figure out the cars final velocity going label. This is a do be in a different color. What is the fun of lossy? Here's the deal. Now that we have four variables, you can really use three of these four to find that fifth. I'm gonna encourage them not to use this displacement that you just found. Because if you screwed up here and then use that wrong value later on defined velocity, you got to get that wrong as well. So try to avoid that. So I'm gonna go ahead and ignore this, and I'm gonna use the same equation I've been using the prior problems. You say V two is V one plus 80. The one is still zero, so it's still just could be a Times T or 2.4 times 12. It's going to figure this out. I'm grabbing 28.8 and that's its final velocity. So it's 28.8 meters per second. Alright. Cole's going the next problem Number five and a slapshot hockey player accelerates the pluck the puck with a velocity of eight meters per second, 2 40 meters per second in the same direction. That's important. That means they're both positive. If the shot takes 3.33 by 10 the negative two seconds, we want to know the distance over which that puck accelerates. So here's an example, which we're not solving for acceleration. We can't later on if we want to, but we certainly do not have to and you know this'll. One is where it starts to get a little bit less obvious as to what equation to use, because plenty of the problems involving acceleration And so here's where we have to kind of think about all our equations and then remember our basic math because there's only one equation that does not incorporate acceleration. And that's that very first equation. Average velocity is changed in distance over time, and V one is not average. The two is not averaged. You can't plug either of these in here. And I see a lot of students trying to do Delta as well. The distant difference between them. That doesn't work either because average and Delta are not the same thing. But if we take that another equation for average velocity, we realize that average velocities actually this some of each individual velocity divide by the number of them. We can first find my average velocity and then plug it into the original equation to solve for dealt the deep. That's the route I'm gonna take. I think it's easiest. You could go and find a first and then find D using a second equation. You're gonna get the same answer. Go ahead, try both. Why not? So I'm gonna do eight plus 40 and I'm gonna take that whole thing in divide by two So 48 divided by two. And that's 24 meters per second. Now I'm gonna I could write that down as a as a known. Why not sure I'll plug it in Over here. Average velocity is 24 meters per second. Ah, but I didn't have to do that as long as they plugged it in appropriately, into my original equation. So first I'm gonna isolate my delta D Delta D is average velocity Times time. Now I'm gonna go in and plugged in, and I'm gonna say 24 meters per second times 3.33 by 10 in the negative. Two seconds. Posit calculated. I'll be right back. All right? This is gonna be a value of 0.799 to relieve it, Aziz. 799 Not 7992 That's perfectly fine. I'm not gonna run it all way up. 2.8. It doesn't really matter. And my answer meters. Getting to be the distance now. This might not make sense. You sell it. Only traveled 0.8 meters. That's not really true. It travels probably far more than that. This is the distance it's traveling while the hockey stick is in contact with the puck, which is not a very large distance. Okay, let's move on to the next problem. Number six. A powerful motorcycle can accelerate from rest. So v 10 to 26.8 meters per second. 26.8 meters per second in Onley, 3.9 seconds. It's time we want to know what is the acceleration and how far it travels. So we're gonna get every single kid a Matic variable in here again. We need three to find all the rest we've got three of. So let's do this. I'm gonna go ahead and say, uh a is changing velocity over time. I know Change in velocity is my final minus my initial all over time, which I probably should ever envy to minus V one. I wouldn't lose any points like this. This is fine, but it's always important to stay consistent. 26.8 minus zero all over 3.9. Let's get allowed me to get a positive acceleration. Let me figure that out. All right. I'm getting an acceleration of positive 6.87 meters per second squared. That's the answer to a And now I could do be confined displacement using any value I have before I said it's appropriate best to not use a calculated value and that answer is still true here, but either which way I'm gonna have to take a second step. I'm either gonna have to do average velocity is distance over time. Find my average velocity. Two men find my distance or I can use the equation Has a in its Since I have a I'm not going to another step of math. I'm gonna go ahead and use that. So I'm going to say, Let's use the equation we haven't used yet. I'm gonna say V two squared equals V one squared plus to a D. As you can tell, there's more than one way of solving these problems so I could have done the d equals V I t . Plus 1/2 a t squared if I want to. And there's a couple others I could have done. So I'm gonna go ahead and rearrange for D. I know my initial velocity zero. So no point in rearranging that I got to get rid of the to a something divide both sides by that And let's see that my displacement is equal to my final velocity squared divided by two times acceleration. So I'm gonna do that. 26.8 and I'm on. Lee, get a square. This. So I'm gonna toss parentheses around this just to emphasize that divide this thing by the entire quantity of two times A, which is the 6.87 I just calculated deposit of your bet. All right, I'm getting a distance of 52.27 meters. Cool. All right, let's jump to this last problem. Okay. Firework shells excited from rest to a velocity of 65 meters per second over a distance of 0.25 meters. That's a delta. We want out how long it took. And we want to know the acceleration. I think in this problem is fine to do the acceleration part for so that we don't have to. That's what I'm gonna do. So I'm gonna say V two squared equals V one squared plus two a Delta D. So my acceleration is simply gonna be V two squared, divided by two Delta D. And that's gonna be the 65 squared, divided by two times 20.25 That's a 0.25 not the multiplayer science. So maybe I should do double parentheses, something like that, just to make it easier to calculate. I'm getting 8450 its final velocity Air Nomsa its acceleration. So that's going to be meters per second squared. Now I'm going to say the time unless the acceleration is changing velocity over time So defined time we just get rearranged that times give the change in velocity over a That change in velocity is giving 65 meters per second and I'm gonna divide by that acceleration I just got Let's figure that it cool. I'm getting 0.769 seconds. That might be more appropriate to move to scientific notation, which is 7.69 times 10 in the negative four seconds. All right, that completes the worksheet. Awesome. Thank you.