Practice: The M40, the U.S. Marine Corps standard-issue sniper rifle, has a barrel length of 61 cm and bullet muzzle speed of 777 m/s. Find the acceleration experienced by the bullet.
|Ch 01: Units & Vectors||2hrs & 22mins||0% complete||WorksheetStart|
|Ch 02: 1D Motion (Kinematics)||3hrs & 11mins||0% complete||WorksheetStart|
|Ch 03: 2D Motion (Projectile Motion)||3hrs & 8mins||0% complete||WorksheetStart|
|Ch 04: Intro to Forces (Dynamics)||3hrs & 42mins||0% complete||WorksheetStart|
|Ch 04: Motion in Two and Three Dimensions||3hrs & 8mins||0% complete||Start|
|Ch 05: Friction, Inclines, Systems||4hrs & 32mins||0% complete||WorksheetStart|
|Ch 06: Centripetal Forces & Gravitation||3hrs & 51mins||0% complete||WorksheetStart|
|Ch 07: Work & Energy||3hrs & 55mins||0% complete||WorksheetStart|
|Ch 08: Conservation of Energy||6hrs & 54mins||0% complete||WorksheetStart|
|Ch 09: Momentum & Impulse||5hrs & 35mins||0% complete||WorksheetStart|
|Ch 10: Rotational Kinematics||3hrs & 4mins||0% complete||WorksheetStart|
|Ch 11: Rotational Inertia & Energy||7hrs & 7mins||0% complete||WorksheetStart|
|Ch 12: Torque & Rotational Dynamics||2hrs & 9mins||0% complete||WorksheetStart|
|Ch 13: Rotational Equilibrium||4hrs & 10mins||0% complete||WorksheetStart|
|Ch 14: Angular Momentum||3hrs & 6mins||0% complete||WorksheetStart|
|Ch 15: Periodic Motion (NEW)||2hrs & 17mins||0% complete||WorksheetStart|
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|Ch 19: Kinetic Theory of Ideal Gasses||1hr & 40mins||0% complete||WorksheetStart|
|Ch 20: The First Law of Thermodynamics||1hr & 49mins||0% complete||WorksheetStart|
|Ch 21: The Second Law of Thermodynamics||4hrs & 56mins||0% complete||WorksheetStart|
|Ch 22: Electric Force & Field; Gauss' Law||3hrs & 32mins||0% complete||WorksheetStart|
|Ch 23: Electric Potential||1hr & 55mins||0% complete||WorksheetStart|
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|Ch 26: Magnetic Fields and Forces||2hrs & 25mins||0% complete||WorksheetStart|
|Ch 27: Sources of Magnetic Field||2hrs & 30mins||0% complete||WorksheetStart|
|Ch 28: Induction and Inductance||3hrs & 38mins||0% complete||WorksheetStart|
|Ch 29: Alternating Current||2hrs & 37mins||0% complete||WorksheetStart|
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|Intro to Motion (Kinematics)||67 mins||0 completed|
|Motion with Multiple Parts||53 mins||0 completed|
|Meet/Catch Problems||23 mins||0 completed|
|Vertical Motion||48 mins||0 completed|
|Intro to Acceleration|
|Vertical Motion & Free Fall|
|Motion On Inclined Planes|
|Motion With Multiple Parts|
|Velocity & Acceleration Graphs|
|Motion Of Multiple Objects|
Concept #1: Velocity vs. Speed
Hey guys, let's get started with one dimensional motion or motion along a straight line or linear motion however your professor might refer to this. I'm really excited to do this video because this is the very beginning of physics it's actual beginning of physics, so let's take a look. Alright so first I want to talk about constant slash average velocity and speed so what's the difference between velocity and speed and what is the deal with constant and average velocity in speed. So first remember we talked about this earlier there are two terms that deal with how much something moves, how much something moves and those terms are displacement which is given by delta X it's a vector so it gets a vector hack it has a direction so it could be negative the other term is distance distance D. It's a scalar so it doesn't have direction and it can't be negative right so displacement and distance again in everyday language they use interchangeably in physics there's a very clear distinction remember just a quick example here if I move 3 and 4 my distance is 7 but my displacement is 5 right so my delta X would be 5 so they're different just like how they're two terms to deal with how much something moves there is two terms to deal with how fast something moves and it's analogous to this situation over here, so the two terms are average velocity so velocity and speed I'll talk about the average portion a little bit later so the difference between velocity and speed has to do with its definition and this is kind of boring but you have to know this really really well. First one is the average velocity is defined as this diplacement over time elapsed but I'm just going to call this time displacement is delta X and this is delta T, delta X remember is X final minus X initial delta T. X up here is measured in meters times is in seconds so average velocity is meters per second velocity is a vector delta X is a vector these guys are technically vectors as well it gets annoying to draw all the arrows so we're not always going to do that but we're defining this so we got to be proper. Speed I'm going to use the letter S, that's not a phi it's an S and it is defined as distance over time and distance again I'm going to call D over delta T and It's also in meters per second alright so I want to point out the difference here this guy is defined in terms of displacement this guy is defined in terms of distance, one is a vector the other one is a scalar. So for example if I say that I am moving with 5 meters per second this is the scalar this is a scalar but if I say I'm doing this at or towards the north. This is a direction and these two things remember combine to form a vector so a vector is a scalar the size plus the direction so that's the difference notice that the vector V is defined in terms of a vector delta X and the scaler S is defined in terms of the scalar D, vector with vector scaler with scaler. Now the distinction between velocity and speed again everyday language use those interchangeably in physics there's a big difference between them one is a vector the other one is a scalar now in terms of the names it's kind of arbitrary they just had to pick a name and say ok the scaler is going to be speed and the velocity is going to be the one that's going to the vector one now I'm not sure why they chose those two the way they did but one way that I remember that you could remember is that velocity vvv vvvv goes with vector so that sounds kind of stupid but it helps you remember. Speed S goes with scalar S.S V.V cool. So if you know the definitions then you I'll pay off in terms of avoiding confusion possible confusion in the end or later on. So negative velocity negative velocity has to do with you moving in the opposite direction remember signs in physics positive or negative have to do with direction now what do I mean by opposite direction and this is kind of silly but you are moving if you go in the negative if you have negative velocity your going opposite to the direction of positive right so usually we say that the direction of positive is up into the right we can change this but if that's the convention that we're using for a particular problem negative velocity just means you're going to the left or you are going down so negative velocity the negative just means direction. Speed's a scalar so it has to always be positive though it could be 0 if you're not moving at all but it cannot be negative.
So that's velocity versus speed now I want to talk about constant and average, so here's the idea at the very beginning of physics we're going to make problems simpler by having no acceleration and let's say you go from you are traveling between two long distances and this is your velocity over time just a quick sketch and obviously you start your car from 0 you reach certain velocity and then there's a bunch of traffic on the way and there's all kinds of crap happens and it looks like that well this is a really complicated problem to solve because it's basically if you're trying to estimate travel time but your computing every time you slow down when you stop on a stop light, so it's way too much so we're going to do in physics we're going to say wow looks like the average of this is about here and we're going to call this the average velocity which will greatly simplify the problems. Now the thing is if you look at this average velocity the idea of the average velocity is that it's a constant velocity and when you have constant velocity problems in physics they're much simpler because there's no acceleration so these are basically the same thing effectively they're the same thing because an average velocity is a constant velocity and so average velocity is going to give you a constant velocity which means your acceleration is 0 now in this situation your acceleration is not 0 but you're basically making it 0 by getting this one number one velocity that's equivalent to all these weird velocities added up and we do that to simplify. So what's good about these problems they're simple because there's only one equation right and it's really hard to mess this up because there's only one equation and that equation is the the one that I just talked about here the average equals delta X over delta T. I want to point out something really important this equation only works if you have no acceleration right this equation only works for you to find your velocity if you have no acceleration otherwise which your finding is you're finding the average velocity not the actual velocity. Sort of another version of this equation is S equals D over T but generally we're going to write it this way and you're going to write V equals whatever delta X over delta T even if you're dealing with speed you just be careful to use the right sign and note to differences between the two, so it's not like there's really two equations we're just going to typically use one. Now what I do want to do so there's this one equation here is I want to write a different another different version of this equation so if you were to expand this X here into X final minus X initial and then move a bunch of stuff around I'm not going to but you can do that yourself you arrive at this equation X equals X initial plus V T it's probably a good idea for you to try going from one to the other its really simple and I'm going to give this a name I'm going to call this the position equation and the reason why I'm giving this equation a name is because we're going to use it later for some stuff and I want to be able to say use the position equation but it's called the position equation because X is your X final, it's where you are X initial is where you started off where you were so this equation says where you are is where you were plus how much you moved plus how much you moved. So that's it so you only have that one equation there's two versions of it but it's really the same equation you don't have to pick equations like you're going to have to later.
So before we actually start on like legit physics problems I want to talk a little bit about the general steps for solving every physics problem obviously this is a very generic guideline but basically most physics problems will start with some sort of text paragraph a little story line and you have to draw and get some sort of diagram right you have to draw your diagram it's going to help what draw as much as you can and then from diagram your going to go to equations so your going to write some equations. From those equations you are going to solve the problem so there's three steps basic steps draw write equations and solve. Now this part here is sort of physics plus like some reading comprehension right so I'm going to just kind of call this English plus physics and then this part here is math and my point is once you have all your equestions you're done physics it becomes an algebra course I mention how physics is math with rules and you know at the of the day it's going to end up just being math and there's a story line that came before that so all physics problems end up being math problems at the end. So the next thing I want to do is again before we jump into actual physics problems. I want to focus on just this part of the equation right here right not going from text to diagram I'm going to give you a diagram and I want to practice getting an equation and solving the good thing about these questions is there's only one equation so it's very straightforward, so these are what I call interval diagrams which is a term I made up and it just means that if you move V you're going to draw a little dot between beginning and end and sort of connect it to a sort of an obvious diagram and put all the information in the diagram and what you're doing usually is you getting this huge paragraph and turning into a picture of consolingly information so you can focus on finding the equation and then solving. So here's my little diagram so I got that it's already been given to me so I have to write an equation the good thing about this section is that there's only one equation so it's just V average equals delta X over delta T. Now very often you're going to see this without your average because it gets kind of annoying to right average average average all the time but remember this V average is only your actual V if the acceleration is 0. If not you technically should be writing average but here we have a constant speed for all of these just to be clear. Constant velocity alright so let's plug in some numbers I'm looking for velocity so I'm going to put a little circle around this so I know that's the one I'm looking for delta X is X final minus X initial delta T is T final minus T initial. Let's plug in numbers this is 20 minus 0 and this is 5 minus 0 so the answer is just 4 meters per second so this was crazy easy right just to get started let's look at this one that that's the final answer. Let's look at this one I have velocity equals delta X over delta T, now I'm given the velocity so let me just write this here 3. Delta X is X final minus X initial divided by T final minus T initial I'm going to ahead and do this this is final minus initial the total time is 5 seconds and we are looking for X 2 or in this case just X final and all I have to do is just move stuff out of the way so that X is by itself this 5 multiplies over here 3 times 5 and then this X not here goes to the other side as a positive and this is what you get over here. By the way that number is a 0 this guy is a 0 so X is simply 15 meters really straight forward let's do another one here. This is V equals delta X over delta T, I know my V my V is 4 my X is X final minus X initial T final minus T initial. So time X final is 20 minus X initial is what I'm looking for and then the time is 7 minus 3 which is a 4 so this is 20 minus X initial divided by 4, let me go away and I'm looking for X initial. So what we are looking for right here so we just got to get this guy alone I'm going to move the 4 over here I got 4 times 4 equals that's just 16 let me just do that 16 equals 20 minus X initial. I want to solve for X initial so I'm going to move it this way so that it becomes a positive and I'm going to move this guy this way so that X initial is by itself on the left as a positive so I get 20 minus 16 equals 4 meters now obviously the actual algebra steps you take don't matter as much as long as you get to the right answer, there's a few ways you could've gone here. So that's it for this one for this intro to one dimensional motion.
Concept #2: Average Velocity Problems
Hey guys, so in this video I want to solve two more problems using constant velocity or average velocity and give you guys a chance to solve two of them as well, so let's get started. Remember first of all that if you move with constant velocity or average velocity remember an average velocity will give you a constant velocity there is only one equation which says that V average is delta X over delta T one equation three variables there's sort of a variation a different version of this equation which says that X final equals X initial plus V T I call that remember the position equation so first example right away here how long would you take you in hours so I want to know what is the time in hours that it would take you to drive from Miami to Seattle right in this is the distance. If you could average this velocity so I'm saying that your delta X again this is going to be our equation your delta X is 3300 miles or you could use 5300 kilometres and your speed your average velocity is 60 miles per hour let me write it like this miles per hour or that's the same thing as 96 kilometres per hour. Now some people here might have the instinct of actually starting here but converting to meters per second because that's what your used to but guess what I'm asking for the time in hours so it's ok to use a velocity that includes hours, and If I were to pick this as my velocity even though miles is not SI unit that's ok too as long as I use this and they cancel so you can use these two together or these two together because it's miles and miles per hour kilometres kilometres per hour what you couldn't do obviously is just connect to the 60 and use it with the 5300 they are completely different units and they won't talk to each other. So I'm going to do it with this one just for no reason the average is delta X over delta T. So if you're solving for time you flip things around T comes up V goes down delta T is delta X over V average and this is 3300 divided by 60 you plug this you put this in your calculator and you get 55 but let me show you the units real quick. Delta X is 3300 miles and this is 60 miles per hour this miles cancels with this miles and this guy at the bottom here goes back up top I want to remind you that 1 over A is actually just A alright. So this is 55 and I get 55 hours which is good news because hours is the unit of time and that's exactly what I want it to be the answer is just 55 straight forward one equation.
What I want you guys to do now is try practise one so what you should be doing is pausing the video giving this is shot and hopefully get it right I'm going to go right into it but you should pause and try this yourself so sound travels through air at this speed here so that means roughly 344 or approximately 344 so I'm just going to say that the speed of sound is 344 that is a constant speed up so but I'm just going to write V constant average you hear thunder about 5 seconds after seeing lighting bolt so here's the idea you're here lightning strikes here and lightning causes thunder but air travels way slower than light so it takes a little while for this guy to get here to you. You should probably draw it this way actually just so that sound is travelling to the right which is the positive direction you don't have to worry about signs so sound travels with 344 and it takes about 5 seconds to get to you and you want to figure out how far is this distance. Now again all you have to do is use V average or just V equals delta X over delta T and now I'm looking for delta X, so delta X is V T. The velocity is 344 takes 5 seconds if you multiply and I have it here it's 1720. Now 344 was meters per second and 5 was in seconds so you get 1720 meters the problem is the question asked you to give this in miles and 1 mile is 1609 meters so I can say velocity I'm sorry rather distance delta X displacement is 17.20 and now I can just convert I want to get rid of meters and into miles 1 mile is 1609 meters and if you do this I have it here is 1.07 miles that's why you might have heard the rule of thumb that for every 5 seconds that it takes for you to hear thunder that's 1 mile away that the lightning struck right. So if it's 10 seconds that the time it takes to get to you is 10 seconds then it was two miles away and so on and so forth. So I'm going to do so I hope you got that right I'm going to jump into example 2 It takes you 50 seconds to go around a circle a radius 50 while running at a constant speed, constant speed means I'm going to be able to use this equation here. Here's the tricky part if you go around a circle your displacement is actually 0 and your average velocity for an entire lap. Is also 0 for one lap because you're back at the same place that's why they talk about a constant speed so here you have to be a little bit more careful if I write this I might be tempted to put the wrong answer so just to be safe I'm going to write that speed is distance over time now if you go around a circle, around the whole circle your distance here your distance here is your circumference, so distance around the circle is circumference. So when you do one lap your distance is 2 pi R so all I got to do is replace this with 2 pi R delta T. I have the radius its 50 meters and I have this time it's 50 seconds the 50's cancel and I'm left with 2 pi so this is 6.28 meters per second. That's how the stuff works again speed they are just looking for the magnitude velocity the average velocity is 0 because you're back at the same place where your speed you're always running with 6. It's just that your running with 6 this way then your running with 6 then your running with 6 this way then your running with 6 this way.
I want you guys to try practice two it's also using circular motion so you go in a circle but it's asking for something a little bit different so you should pause the video give it a shot hopefully you get it, I'm going to jump into it the other circle of radius 30 and you move around it with a speed I'm going to put S equals 5 and then its asking how many laps do you complete in two minutes? So for a delta T of 2 minutes which obviously that's 120 seconds it wants to know how many laps. Now I don't want to talk about the whole idea of how many laps just yet, first what we are going to do is figure out what kind of distance did you move and then we'll try to convert distance in two laps later. So distance speed equals distance over time and I'm looking for distance so distance is speed times time and notice how T and delta T are kind of used interchangeably that's fine speed is 5 and time is 120 and this gives you 600 meters so the total distance that you went around this thing is 600 meters. Here's the idea one lap equals to 1 circumference of distance so it equals to 2 pi R and it has a unit of meters so one lap converts to meters using one lap is 2 pi R. So if I want to go from what I can do is I can go for meters to laps, right its a conversion so 2 pi R meters equals one lap just think of lap as a unit and then this M here cancels with this M and I'm left with laps. So this is going to be 600 divided by 2 pi 30 and if you put this in a calculator you get 3.18 and that is has units of laps, 3.18 laps so that's how you do that. Anyway that's it for this page, hope you got that right let's go onto the next one
Concept #3: Acceleration & Motion Equations
Hey guys, so in this video I want to talk about acceleration as well as introduce you to do the three to four equations of acceleration. That's going to be the foundation for most of our motion problems also known as kinematic problems so let's get on it. Acceleration is given by the letter A and it's the finest change in velocity over change in time, velocity is a vector, acceleration is a vector. Change in velocity, the delta notation, is V final minus V initial and divided by time. Velocity is meters per second and time is seconds so you can combine this you get meters per second square and you should absolutely remember that that's what the units are. Acceleration is always a vector, always a vector, let me talk about that for a little bit. If you remember when we're measuring how much something moves there are two words, there is distance and displacement. One is a scalar the other one is a vector and if I'm measuring how fast something moves there are also two words speed and velocity. Now these two guys are associated with each other and velocity is defined in terms of delta X. Now in terms of acceleration there's only acceleration and there's only a vector that's what I mean by always a vector. There is no scalor equivalent of acceleration like what you have with velocity and displacement delta X. Acceleration is always a vector. Now one thing that people will get confused with sometimes is that the positive if you have a positive acceleration it doesn't mean necessarily that you're speeding up. What it means instead is that velocity is becoming more positive and I need you to remember that. Positive acceleration means your velocity is becoming more positive like what you see with distance and displacement and speed and velocity in everyday language we use these words kind of interchangeably loosely just like how in everyday language acceleration if you're accelerating it usually means that you're speeding up but in physics we have to be careful with these because it's a little bit different. Acceleration has to do with velocity not with speed so speeding up means that you're becoming faster and it does not necessarily mean that your velocity is, that you're velocity's becoming more positive. It doesn't necessarily mean that you have a positive acceleration and slowing down if you're becoming slower it means that your speed is going down not the velocity. Remember velocity is a vector, so velocity is comprised of because it's a vector it's a magnitude whatever the number is and that number magnitude is speed and a direction. So if your speed changes you could change one without changing the other basically let me jump in to show you some of the stuff right away. So for example if I'm going from -3 in terms of velocity, this is a number line showing the velocity, and if I go to the right of the number line I am becoming more positive so my velocity is increasing or becoming more positive I should say and my acceleration is positive. Let's say I go from -3 meters per second to -1 meters per second, what's happening here? I'm going to the right of this line so my acceleration is positive however my speed is decreasing, why? Because speed is a scalar it doesn't care about signs it's just a number. I'm going from 3 to 1 ignore the signs and obviously 3 to 1 you're getting smaller, so your speed is decreasing so you are slowing down but you have a positive acceleration right? Weird.
So anyway there's all these kind of different things so I told you that acceleration grows to the right well speed grows this way. This if you're going from zero to the right your speed is growing, if you're going from zero to the left your speed is growing as long as the number forget the sign if the number's getting bigger. The flip of that is if you're going towards zero from the left or from the right that means your speed is going down, you are becoming slower. Here you are becoming faster so again speed and velocity, different things, faster and positive acceleration different things this is kind of tricky but I want to get this out of the way now rather than you be confused for some portion of the course. The best way to do this is just with examples let's do this one. I'll do the first one I want you guys to try the second and the third. So I'm going from positive 2 to -5. Always draw as much as possible, so zero, positive 2, -5, a little velocity number line if you will and I'm going my initial is positive 2 and my final is -5 so I hope you see here that since I'm going to the left my acceleration is negative and what about my speed? Look at the number I'm going from 2 to 5, it doesn't matter that it's positive or negative that number is increasing. Again negative acceleration but my speed is increasing. And by the way as we're going to zero from 2 to zero, your speed is actually decreasing and then from zero to 5 your speed is increasing but what matters is not what happens sort of in between you just look at the very beginning and at the very end and you went from 2 to 5, your speed is increasing. That's the first one, I'm going to do the second one over here just kind of making some space and then we'll do the third one here. So B, I go from -2 to -5 let me draw that, -5, -2, 0. I'm going from -2 to -5. Most of the numbers are the same I just kind of messed around the signs a little bit to see how this works. -2 to -5, I'm going to the left in the velocity line so my acceleration again is negative and my number's going from 2 to 5 forget the signs so my speed is again increasing so it's you know effectively the same answers even though the numbers are a little bit different. C, -5 to -2 let me draw that here's -5, -2, here's zero and -5 to -2 goes like this. I am going to be right so I'm becoming more positive you're getting more and more towards the positive so my acceleration is positive. My speed however is decreasing because I'm going from a 5 to a 2. The number, forget the sign, the number is becoming smaller. So hopefully that makes sense. There's some other stuff with this that I'm leaving for us to talk about later, for now I need you to remember that a positive acceleration has to do with becoming more positive not necessarily with speeding up and that speeding up, slowing down actually has to do with speed. That's the first half of the video, now we're going to get into the equation part. Let me show you guys some equations. So remember we talked about this if your acceleration is zero then you have a constant velocity which might be an average velocity and then we have this equation, this is the only equation you have. You have one equation. Now I showed you that there is sort of a, you can write this equation in a different way and it looks like this, move some stuff around X equals X initial plus VT and I told you the reason this is relevant, this equation, is because we're going to use these in some problems I'm going to call this the position equation and it's really the same equation two versions but that's if your A is zero. If your A is not zero you're gonna have four equations of motion and then you're going to have to get into the whole deal having to pick the right equation. The reason why there's a star here is because some professors will give you three, some professors to give you four. If the professor gives you four you can use all four, if the professor only gives you three equations that fourth equation you may or may not be able to use. If your professor is very picky about you only using stuff he gives you then you have to stay away from the fourth equation, that extra fourth equation. If he doesn't care then you can use it. So that's why this fourth equation when I listed here, I'm going to call it the extra equation and we'll get to that in a little bit. So I call these the equation of motion but they're also referred to as kinematics equation. Kinematics is just the study of motion, that's the fancy physics word and another name for these is they are the UAM equations and it just means uniformly accelerated motion. In all of these problems it's assumed that your acceleration A is constant. So in most of physics your acceleration is constant. If your acceleration is not constant these equations won't work so your acceleration needs to be constant or average. If you are not told otherwise you will assume that your acceleration is constant so what I want to do real quickly showing these equations I have a particular list, a sequence for them and I'm going to list the easiest one first, the easiest one to sort of play with to manipulate, and the hardest one last. Easoest to hardest because if you are trying multiple ones you're gonna start with the first one. So this is V equals V initial plus AT, this one is V squared equals V initial squared plus 2A delta X, and this one is X equals X initial plus V initial T plus half of AT squared and the third bonus one is delta X equals V initial plus V over 2 times time. I'm not going to get into how these equations come about your book might derive that, it doesn't matter. You just have to know how to use them. I do want to show you one thing about these equations before I kind of get into this part of the chart which is that this equation here can be rewritten and I'm going to call this equation 3 I don't know B or whatever. If I move this X initial to the left I get X minus X initial that's delta X so I can write this as delta X equals V initial T plus half of AT squared. There's less stuff if you do it that way this is usually how I'm going to write this equation. Most of the time the initial position is zero anyway so it doesn't matter. Now if you look through all these equations and you kind of make a list of all your variables, you're going to see that there are seven total variables but these two guys really are they just form delta X. Delta X is X final minus X initial and since I'm using delta X here and delta X here and delta X here, I'm going to consider that these five here are the five main equations I mean variables. So I have five variables. A very important thing to know about these problems is that to solve any kinematics motion problem you're going to need three out of five and I need you to remember that, hey that's cheesy. So you need to have three out of five. Every motion problem is going to have a little story line, the zebra's running, the lion's coming, something stupid like that and you need to extract three out of five variables out of the text. If you can't find three, you're missing something most of the time.
So what I want to do now is show you how these equations have sort of different combinations of variables and depending on what you have you're going to pick different equations and I'm going to show an easy method to pick those. So this equation I'm going to do this real quick has V initial, V final, acceleration and time. It doesn't have delta X. I'm going to put a little sad face here. This one has V initial, V final, acceleration, delta X but it doesn't have time, sad face. This one has these two guys therefore it has delta X, it has V initial, it doesn't have V final, sad face, it has acceleration and time. This one has delta X, V initial, V final, time but no acceleration. Notice that every equation is missing something except that all of them have V initial. I'm going to talk about that first. If you have a situation where for example you're not being given V initial, something is missing these equations just seem not to be enough, you can always just use a combination of two equations. So you can find one other variable and then solve it using using one equation find one variable and then now we have enough information to use another equation to find what you need. At the end of the day a lot of physics questions are just about hussle, you just have to you know you have all these equations just plug it in keep going at it but I will show you a more systematic way of doing this. Now before I talk about how to pick your equations there's basically three ways I want to show you what happens with all of these guys if your acceleration is zero. Remember we're talking about problems where acceleration is not zero, it's a more complicated problem but we just have mentioned how it's much simpler if our acceleration is zero. So let's look at this equation here, if acceleration's zero and try not to make a mess on your notes I'll make a mess here but I'll delete. I'll go back so this is gone so I have V equals V initial and so that's kind of silly because if there is no acceleration that means velocity doesn't change so this equation doesn't really tell us anything, it's useless it doesn't give us new information. Velocity final equals velocity initial. We knew that. Here same thing happens this cancels because A is zero or if A is zero and then I just get that V squared equals V initial squared, again useless. The third equation is going to cut out this guy here so let me write this X equals X initial plus VT so that's not necessarily useless in fact I want to point out that this equation is the same as this one which was an equation where acceleration was zero. They're the same equation they just kind of simplify from one to the other so I'm going to call equation number three over here our position equation. I'm going to kind of put this here. Equation three is our position equation. So there are two versions of the position equation, this one and this one but it's actually the same exact equation you can always start from here from number three and then if you have no acceleration you can just do that and that's my point with doing this. I don't want you to think that for some problems you get this and then for some problems you get this. These four equations always work except that if your acceleration zero just cross it out and then the equation is simplified. Some of them will become useless because they won't really be able to help you they'll just tell you the obvious, some will be useful. So this equation here has no A but even that equation works as well and I can show you that real quick. If you have no acceleration these two guys are the same so I can just call this V and I can say V plus V is 2V divided by 2. That 2 cancels and I have a T, delta X equals VT. If you move it around you have V equals delta X over delta T. Just kind of play around with these to show you, get you guys a little bit more comfortable with it so that equation still works it just kind of becomes V equals delta X over delta T and guess what? That is this guy over here. Let me just kind of do some color coding here, looks pretty. So how do you know which equation to use? People struggle with this. So there's sort of the brute force approach don't know try all of them and that's why I list them one, two, three. I'm going to show you how to do it in an easier way but let's say you forget. Well just do all of them until you get something. Try the first one first because it's easiest and then wait for the last one. Do the last one last. Now the third one is hardest because it's got more things in it, it's got a square but also sometimes you might get a quadratic equation out of it. It's the more tricky one potentially a quadratic equation that sucks but it's also the most useful one so that's kind of messed up. First way we're going to do it is try everything right and then that's always going to work. The second one is kind of obvious instruction set which is first of all the equation must have your target variable for example equation number two doesn't have time it's missing time so if you're looking for time you can use equation number two I don't care what you put in there are time's not going to come out of it it's not there and you have to not only must be your target variable to be there but it has to be the only unknown. So if I'm looking for time here but I don't have A and I'm stuck with two variables that's not good either. So these are sort of the two obvious points. There's a third way and that's my favorite and we're going to use what I call let me right this down first then I'll explain what I mean. We're going to have the what I call the ignored variable. The ignored variable will determine the equation.
So first of all what do I mean by the ignored variable? All of these problems there are five variables and you need three. You need three out of five, needs three out of five. Well all of these problems will give you three, ask for one and they will ignore one. In other words they won't give you that value and they won't ask for it either. For example I give you delta X, VI, V final, I ask for A. My ignored variable is T. It's the one that, I'm going to put a little side face here, it's the one that I didn't give you and I didn't ask you for I just don't care about T. So I'm going to use if T is my ignored variable, I'm going to use the equation that ignores T, that doesn't have T. Equation number two. So if T is ignored I'm going to use equation two because it's the one that ignores T. So let's do some problems real quick and then you get the hang of it. A car, again I need three out of five, a car starts from rest and moves with a constant 5 meters per second squared. You need to know that this is an acceleration. The method that I'm going to use to solve these problems is very straightforward I call this listing it's silly but it helps listing to your children. I just completely made up. Don't call me on that and basically what I'm going to do is you have five variables and you want to make sure you don't lose track of anything so I'm going to list them. So you have five kids now, V initial, V final, A, delta X, delta T and the reason I'm doing this is just to get our work organized and so we can have one systematic way of solving all these problems. I need three out of five, once I have to three out of five I'm good to go. Starts from rest means that the initial velocity is zero. A constant velocity of 5 and look at what A is asking here this is part A. It's saying find the speed after 15 seconds. I'm telling you that delta T is 15 and I'm asking for the speed. Now with speed you have to be careful because there are two speeds which one is it asking for? Well it's asking for the speed after 15 seconds so it's asking for your V final. Another way to figure this out is that your V initial you have it is zero so that's what I'm asking for. Notice how I have three values, I'm asking for V and delta X is neither asked nor given so I'm going to put a little sad face there delta X is my ignored variable so go to the table and look at the equation that doesn't have a delta X. The equation that doesn't have a delta X is the very first one. Obviously not going to have this table during the test but you should have the equations whether it's given to you or you're going to have to memorize them and just by looking at these equations you can quickly see look at the first one there's no delta X there. So this tells me that I'm going to use equation number one. Now these numbers are numbers that I make up so that I have a certain sequence. Professors will use different orders of equations it doesn't matter what I say one is like my version of equation one. So V equals V initial plus AT, initial velocity is zero, acceleration is 5, time is 15 and this is 75 and the unit's obviously meters per second. I want you guys to do part B, very similar process I want you to list your children. The variables are here and then I want you to plug in all the numbers. So pause the video and try this out you need to be good at this I'm going to keep going. Your initial velocity is still zero because it's still this part of the problem but now it's jumping to part B instead. So initial velocity is still zero, final velocity, acceleration is still 5, delta X, delta T. Look what it says. I want the distance that's delta X after 20 seconds, that's 20. I know three variables, I'm good to go. Now notice how the question's asking for distance not displacement but it's okay because we're going to solve using distance displacement but we know that it's actually meaning distance. Notice how these equations all have delta X displacement not distance and they all have V velocity not speed. We don't have to memorize them with different letters for different situations. So just know that this is actually distance. Here we're just moving to the right so it doesn't matter direction it is not an issue here. The variable that's being ignored is V, so I'm going to put a little sad face there and then I just have to use the equation that doesn't have a V final and if you look through your equation list it's the third equation. So delta X equals V initial T plus half of AT squared, your V initial is this so half acceleration's 5 times 20 squared if you put this in calculator carefully you get 1000 meters. You get 1000 meters. So anyway that's it, this is the foundation of kinematics. You have to practice this and get pretty beast at it. Alright so we're done for this one.
Concept #4: Motion with Acceleration (Practice Intro)
Hey guys, so now that I've introduced the basic idea of acceleration and shown the three or four equations you are going to be using I want us to do some practice problems before we start I want to just put what the equations are and I want you guys to try these out so let's do it.
Practice: The M40, the U.S. Marine Corps standard-issue sniper rifle, has a barrel length of 61 cm and bullet muzzle speed of 777 m/s. Find the acceleration experienced by the bullet.
Practice: A car leaves a skid mark of 70 m while coming to a full stop. Assuming a constant deceleration of 8 m/s^2. What was the car?s initial speed?
Practice: A car accelerates from 30 m/s to 60 m/s in 5 seconds. What distance does it cover in that time?
Practice: The 2013 Ferrari California?s quarter mile time (time to travel one quarter mile, or 402 m, starting from rest) is just 12.0 seconds! Assuming constant acceleration, how fast will it be moving once it reaches the quarter mile point?
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