Uniform Accelerated Motion (UAM) Examples

Corey Mousseau
A free video tutorial from Corey Mousseau
New York State Master Teacher in Physics
4.6 instructor rating • 14 courses • 2,770 students

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Physics - Kinematics for High School and AP Physics 1

This is a comprehensive Algebra based Mechanics course in physics specifically covering topics of Kinematics.

05:03:24 of on-demand video • Updated August 2020

  • Understand the major concepts of kinematics in 1 and 2 dimensions.
English [Auto] All right we go Mousseau here. We're going to go through some you am example problems. All right let's go through the whole process is as clear and concise I possibly can. So first step read a problem. So we have an Olympic class sprinter starts a race with the acceleration of 4.5 meters per second squared. What is her speed 2.4 seconds later. First job done. Second step. Make a list. You can write unknowns out or you can just simply make a list. So I want to go through it 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 4.5 meters per second squared. We want to her speed 2.4 seconds later. Here's what a lot of students said they read the number the scans gets in number and they look way before his speed. So they go ahead to rate 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. Well before I make my unknown yet remember we need three variables to find every other variable. I only have to hear this thing else I need to read in 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 velocity her final velocity. You can rate V to vi. 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 kinematics 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 to make sure I'm keeping track of all five. OK. So for now I'm just going to look at these top four. Now what we've got to do is we got to think about those UDMA equations and think well what equation incorporates these four variables. Now normally I do not encourage you to look up your equations. I'd rather you just know them if you've got a resource in front of you. Go ahead look at it. Take your time look at it. You probably eventually saw V.F. equals VII plus 80. Now I'm writing it down the format that you probably have in your notes but no one does. I put one in two here and I did that on purpose. The first and the second speeds not the final and initial It's really totally ok to do one in two but it's probably smarter to put that in your equation. So instead of v v 2 that's the final velocity instead of vi on that one because 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 too. So now we've got to do is that too. It's important to substitute in your units as well. 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 all get pretty lazy early on and I'll stop doing it as long as I've done it once. I typically don't do it again but it can be very helpful to determine your final units. All right go ahead and solve this on your own. I'm going to go ahead and I'm going to solve it as well. OK if you have not had enough time to solve puzzles I'm about to tell you the answer. Ok the answer is ten point eight for the magnitude in 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. You to take the opportunity to 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 with units you don't have to sub in with units. If you made a noseless with units I think it's essential to make a Gnome's list and I think it's equally essential to include units. So at that point since you've done that something in with units is optional get. Let's move on. Number two a well thrown ball is caught in the well-padded MIT. If the deceleration of the ball is two point one times ten of the four meters per second squared and one point eight five times ten and the negative three seconds elapses from the time the ball first touches the it until it stops. What was the initial velocity of the ball. Well let's make your knowns list. We know the ball has a deceleration that implies that it's causing the object to slowed down and I'm to treat the forward initial velocity as positive as a result. I'm going to refer to this value as a negative it's acting against my forward motion. So when I say the acceleration is 2.1 times ten to four meters per second squared. We know that 1.5 by 10 and in three seconds the lapse of my time elapses from the time the ball first touches the Met until it DOPs that's the hidden variable stops. That's at the end its final velocity is zero. We all know the initial velocity of the ball. All right go ahead. Think of the equation you use positive for any more time I'm about to read it down. Yep it's the same equation we just did. V.F. equals VII Plus a T. My final the zero so I can solve it in a zero or I can just cross it across. So I need to isolate vi to do that. I'm going to subtract 18 on that orated in right now but I often don't write in my math. So I think you should be proficient enough to be able to do this on your own vi will equal negative a T. Now I need to substitute in it's negative 8 times t negative is part of the equation not part of the variable. I do need to include Oh that. I said it out loud but I didn't write it down earlier. The deceleration is acting against its forward motion in some column this negative I should have written that negative in. Sorry about that my initial velocity is negative times negative which is negative 2.1 low by 10 of the four I'm putting parentheses around it just so you can not jumble up are negatives and then times my time 1.5 times 10 the negative 3. Look at it just like I said I'm going start getting lazy not putting my units in. That's OK because I already did one over here. Now I'm going to plug in my value my negative will cancel out this negative which makes sense that means the ball isn't 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. Thirty eight point eight five and it's velocity. So my units are meters per second. Let's move on to the next problem. Three a bullet and a gun is accelerated from a firing chamber to the end of a barrel at an average rate of six point two by ten to five meters per second squared for eight point one batsman in 84 seconds. What does its muzzle velocity. In case you don't know that it's the final velocity it can list a six point two by 10 in the five meters per second squared. Time is eight point one by ten in the negative four seconds if it's boats being excluded from the garden so what's it starting velocity. It must be zero right. V-1 is indeed zero. V-2 is what I'm looking for. Once again same equation V2 equals V-1 Plus a T. We want is zero. So therefore V-2 is simply 8 times T which is that six point two by 10 of the five times the 8.1. I tend to the negative for let's figure this out positive. All right I got an answer. Five hundred and 2.2 meters per second. Sharpes you know doublechecked make sure it makes sense it shows you know acceleration is positive. Obviously for us it's going to increase in speed in the positive sense. So bullets can be used in a pretty high speed this is pretty legit. Let's move on. Number four it while entering a freeway a car accelerates from arrest I'm going to go ahead and put my nose in as I go now. So Karch So it's from us that means its initial velocity is zero at a rate of 2.4 meters per second squared for 12 seconds. We want to know how far the car travels and B what its final velocity is Rigaud we're going to actually find every single one of the motion variables. Let's do the displacement first. We're looking for any equation that has V-1 in it has time in it and it has acceleration and it sometimes you have to use two equations in this case we don't. We're going to use change and displacement is equal to V I T plus one half a t squared my initial velocity zero zero times time is zero. This whole term goes away. That's often the case in this equation. That's good helps her math me a little bit easier. So my displacement is simply one half a t squared that's going to be one half of a two point four 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 properly as I do these examples. You should do them as well. Make sure you're getting the same answer that I'm getting. If you're not either on wrong which is possible happens all the time or you're wrong. Which is probably as well. So make sure you actually practice this. I'm going to pause this while I figure this out. You should as well. OK I got an answer of one hundred and seventy two point eight. And that unit is meter's because we're dealing with distance or displacement. Cool. The answer today. Now for B we want to figure out the car's final velocity. Go and label this as a do in a different color. What is the fun of Aussie. Here's the deal. Now that we have four variables you can really use three of these four to find that fifth. I'm getting encouraging not to use this displacement that you just found because if you screwed up here and then use that wrong value later on. Define velocity you get to get that wrong as well. So try to avoid that. So I'm going to go ahead and ignore this and I'm going to use the same equation I've been using on the the prior problems. Lucy V-2 is V-1 Plus a T. We want to start zero. So it's just going to be eight times tea or 2.4 times 12. It's going to figure this out. I'm grabbing twenty eight point eight and that's its final velocity so it's twenty eight point eight meters per second. All right calls go in the next problem. Number five in a slapshot a hockey player accelerates the puck the puck with the velocity of eight meters per second. To 40 meters per second in the same direction at some point that means both positive the shot takes three point three three by ten. The negative two seconds. We want to know the distance over which that puck accelerates. So here is an example which we are not solving for acceleration. We can later on if we want to. But we certainly do not have to. And you know this one is where it starts to get a little bit less obvious as to what equation to use because plenty of the problems involve an acceleration. And so here's where we have to kind of think about all the equations and then remember our basic math because there's only one equation that does not incorporate acceleration and that's the very first equation average velocity is change in distance over time. And V-1 is not average. V-2 is not average so you can't plug either of these in here and I see a lot of students trying to do Delta as well the distance 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 velocity is actually the sum of each individual velocity divided by the number of them. We can first find my average velocity and then plug it into the original equation to solve are dealt the D. That's the route I'm going to take. I think it's the easiest route you could go and find a first and then find D using a second equation. You're going to get the same answer. Go ahead try both. Why not. So I'm going to do eight plus 40 and I take the whole thing and divide by twos of 48 divided by two and that's 24 meters per second. Now I'm going to it I could write that down as an unknown. Why not. Sure I'll plug it in over here. Average velocity is 24 meters per second. But I didn't have to do that as long as they plugged it in appropriately into my original equation. So first I'm going to isolate my Delta d Delta D is average velocity times time. Now I'm going to go out and plug it in and I say 24 meters per second. Times three point three three by ten and the negative two seconds. Posit. Calculate it. I'll be right back. All right. This is going to be a value of zero point seven 992. Leave it as 7 9 9 7 9 9 2. That's perfectly fine I'm not going to run up to a point. Doesn't really matter. And millions of meters in the distance. Now this might not make sense. You say it only traveled point eight 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. OK let's move on to the next problem. Number six the powerful motorcycle can accelerate from rest. So one is zero. Twenty six point eight meters per second or twenty six point eight meters per second. In only 3.9 seconds this time we will know what is the acceleration and how far it travels to get every single kinematic variable in here. Again we need three to find all the rest. We've got three. So let's do this. I'm going to go ahead and say a change in velocity over time and no change in velocity is my final minus my initial All over time which I probably should have written V-2 minus V-1 I wouldn't lose any points like this. This is fine but it's always important to stay consistent. Twenty six point eight minus zero all over 3.9. That's going to allow me to get a positive acceleration and we figure that out. All right. I'm getting an acceleration of positive six point seven meters per second squared. That's the answer today. And now I can do a b. I can find displacement using any value I have before I said it's appropriate best to not use a calculated value. And that answer still true here. But either which way I'm going to have to take a second step. I'm either going to have to do average velocity distance over time find my average velocity to then fly my distance or I can use an equation has a in it since I have a I'm not going to do it another step of math. I'm going to go ahead and use that. So I'm going to say let's use the equation we haven't used yet. I'm going to say V-2 squared equals V1 squared plus two a D as you can tell there is more than one way of solving these problems. So I could have done the Eagles V if us one of 80 squared if I wanted to and there's a couple of others I could have done. So I'm going to go ahead to rearrange for D. I know my initial velocity is zero so no point in rearranging that I've got to get rid of the to a something or divide both sides by that I'm going see that my displacement is equal to my final velocity squared divided by two times acceleration. So I can do that. Twenty six point eight. Only get a square this I'm going to toss parentheses around this just to emphasize that divide this thing by the entire quantity of two times a which is the six point seven. I just calculated posit that I am getting a distance of fifty two point two seven meters. All right let's jump to this last problem OK. Fireworks show is accelerated from rest to a velocity of 65 meters per second over a distance of point to five meters. That's a Delta. We want to how long it took and we all know the acceleration I think in this problem is fine to do the acceleration part first although we don't have to. That's what I want to do. So I'm going to say V-2 square equals V1 squared plus two a Delta D. So my acceleration is simply going to be V-2 squared divided by 2 Delta D. And that's going to be the 65 squared divided by 2 times point to five point to five. Not the multiplier science. Maybe I should do double parentheses something like that just to make it easier to calculate. I get getting eight thousand four hundred and fifty and that's final velocity. No I'm sorry its acceleration. So that's going to be meters per second squared. Now I'm going to say at the time I guess the acceleration is change in velocity over time. So to find timing just get rearranged that time will give you the change in velocity over a change in velocity is give me 65 meters per second. Then divide by that acceleration. I just got Let's figure that up cause I'm getting zero point zero zero seven six nine seconds. That might be more appropriate to move to scientific notation which is seven point six nine times ten in the negative four seconds. All right. That completes the worksheet. Awesome. Thank you.