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2.1 - 2.3 Video Lesson

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hello AP Physics today we're going to introduce chapter 2 and discuss sections 2.1 through 2.3 the title of chapter 2 Motion in one dimension and the goal is to describe and analyze linear motion linear means line so in this chapter we only discuss Motion in a straight line either horizontal motion or vertical motion  string class you watch the pre-lecture video motion along a straight line please access the masteringphysics site to view this video when representing position we're going to use an x-axis to analyze horizone horizontal motion and motion on a ramp what's a positive end to the right so when you're to the right of the origin represent that with a positive X and when you're to the left is the origin a Negative X  likewise we will use the y-axis to analyze vertical motion with pawsitive in up so when you're above the origin or prison with the Positive lie when below  a negative y please take a look at the motion diagram represented this can represent the motion of a student walking to school for the first part of the trip they're walking along and about at the 200-meter Mark the student slows down and gets pretty close to stopping they must cluster late for school and then they run the rest of the way please note that the velocity vectors at the end of the trip to school or longer than the call Steve actors at the beginning indicating the student was going faster at the end of their trip  also every. In the motion diagram of figure 2.2 represent the position at a particular time we can now office information on a position versus time graph the please note that the position versus time graph is not a picture emotion is just another way to represent the motion of the student let's take a little let's look a little closer at this graph the first thing we're going to always want to do when studying grass is to identify what kind of graph were looking at in this after we will learn about three different kinds of graphs position versus time graphs velocity versus time graphs and acceleration versus crafts  in this first graph on this position versus time graph we note that the faster speed corresponds to a slope looking at the students motion as they went to school at the second segment is when the student slows down is the slope of the graph decreases while the last segment shows the steepest slope which indicates she was increasing her speed at that point  the slope of the object's position versus time graph will always be the object velocity at point in the motion  the slope is determined by the rise divided by the Run for the segment of the graph that you're studying please also remember that each slope will have a sign and a slope that shown represented a positive slope when you take the rise over there you can say that they went 300M in three Meat and three minutes so the slope would have been 100 meters per set  here's a quick check to see if we can use a motion diagram to represent the correct position versus time you'll want to pause the video to get your answer and start the video again when you're ready to hear the correct answer here's a motion diagram of a car moving along a straight road which position versus time graph matches this motion the correct answer is e the first thing we need to note is on are on our coordinate system the origin is located here so emotion actually started to the left of the origin so we need to indicate that our position started out at A- Scott which would have wiped out answers a Andy both choices B and C also started with a negative position so at this point we need to look a little bit and it's a Lil Bit Closer at her motion diagram also noticed that at the beginning it ended it's a slower velocity and at the end indicates a faster or a higher velocity so since on a position versus time graph the slope is indicated by the velocity we need to have a more shallow slope at the start and a steeper slope at the end which is indicated by choice we can also deduce velocity versus time graph from the position versus time graph the velocity versus time graph is yet another way represent the object's motion to do this we will take the slope values of the position versus time graph when they become the Y values of the Velocity versus time graph in the first segment shown here the slope is positive and a constant 60 meters per minute which equals 1.0 meters per second so since the velocity is positive and constant will represent it with a positive 1.0 velocity this time frame  looking at the second set segment during this segment of motion the slope d but it's still positive calculating the slope we can see that the velocity is possible with the smaller magnitude which is indicated by this segment  we can also take a look and see that the third segment is the steepest so it should indicate an even positive velocity on our velocity versus time graph you always look at the access to determine what kind of grass you're studying  we can also work backwards and be able to deduce a fission versus time graph from a velocity versus time graph the sign of the Velocity tells us whether the slope the position versus time is going to be positive or negative and then the magnitude of the Velocity Tales this how steep the must be so starting with a velocity versus time graph if we study this segment As you move away your velocity is positive 1.0 meters per second so the slope of our position versus time graph have a positive slope that is calculated to come out to one meter per second so we went 15 meters and 15 seconds when we returned your valet what is a -3 meters per second so the slope of your position versus time graph needs to be -3.0 indicated by the negative slope and if you calculated the slope here it would come out to 3.0 meters per second also  let's take a look at an example figure 211 give the position versus time graph of a car brass a draw the car's velocity versus time graph  so we're going to make our graph velocity versus time and we're going to want to make sure that as we go along we're going to want to indicate the correct so here would be 2 seconds hand here would be about 4 seconds and then six seconds so the first thing that we're going to need to do is to calculate the slope of each segment so that we get the value that we want a graph on the velocity versus time graph  since slope is rise  overrun I noticed that for the first segment we would have a negative four minus zero over a run of 2 - hero which will give us a slope of a -2 m per second so since the slope indicates the velocity for the 2 seconds will need to come down to the negative 2  Under the Velocity in graph a horizontal line -2 to the 2 seconds  the second segment  shown that all segments if we wanted in indicate that this one will segment a you notice that there is a zero slope there is no steepness so from 2 to 4 seconds neck graph a velocity of  0 then segments C to calculate the slope rise over run we will have six- and -4 over your run six- 6 - 4 seconds which will give us a 10 /  2 or a positive 5 meters per second so I have to go to your fat positive five velocity and indicate that for the last  segment so now we need to describe the car's Motion in words we could say that the car moved to the West 2 meters per second for 2 seconds then stopped for 2 seconds and finally turned around and drove East at 5 meters per second for 2 seconds  noted the value of our slope determine the speed and the sign of our slope determined the direction he's got a quick chick which velocity versus time graph matches this motion diagram please note that these are Velocity versus time graphs not position versus time graphs video if needed the correct answer will be D taking a look the origin is located here so the velocity vectors are moving to the negative Direction so we a negative velocity it starts out with a very small velocity at the beginning and it has a much larger velocity at the end so graph D First shows a negative velocity that increases in the negative direction for the second segment  here's another quick check a graph of a position versus time for a basketball player moving down the court appears as follow which of the following Bluff City grass matches the position graph shown pause the video now if needed the correct answer for this quick check is C position vs. time graph the first segment shows zero slope so we needed to have a zero velocity for the first segment would have eliminated a but keeping b c and d available the second segment would have indicated a negative which would have meant we needed a negative velocity knocked out D because you have a pause velocity but the reason B is incorrect as be showing that the velocity is changing well we have a constant hair it means you have a constant velocity which is only indicated by choice C take a look at it next quick check which velocity versus time graph goes with this position versus time graph the correct answer is C take a look at your position versus time graph you will see that you have a straight segment here which means you have a constant slow in a constant slope indicates indicates a constant velocity  but at the end you see that the slope is tapering off becoming less shallow so this indicates that the speed is decreasing we are getting slower so the only grass that showed started with a constant velocity would have been C&D but since it's a positive we would have known you had to have a positive velocity that tapered off still in a positive direction but was getting closer to 0 straight-line Motion in which equal displacements occur at any success equal time intervals is called uniform motion or constant velocity motion an object's motion is uniform if and if its position versus time graph is straight  the displacement between two successive frames are the same the dots are equally spaced as shown in the motion diagram this is represented in the position versus time graph below has a straight line the slope of the line is going to be equal time increments and straight  so what what straight lines on constant slope or what straight lines which means cost of slope means on a position versus time graph in the first position versus time graph a positive slope indicates a constant velocity moving away well in the second it's still a straight line which indicates a constant negative slope which mean does it cost of a lost you moving the motion detector or towards some site so anytime you have a straight line on a position versus time graph it indicate a constant velocity whether you have a positive slope or a negative slope indicates which way the object is moving away from the source or toy the source and finally if you have zero slope it indicates that the object is not moving the velocity of an object in uniform motion tells us the amount by which its position changes during each second the displacement or Delta x is proportional to the time interval delta T this is just another way to write the formula were given in chapter one which is the velocity is equal to the displacement are change in position over here's a quick question for you to take a look at this is when the 10 km per hour bikes are 20 kilometers apart Abby begins flying from one wheel to the other at a steady speed of 30 km per hour when it gets too wheel it abruptly turns around and flies back to touch the first wheel and then turns around and keeps repeating the back and forth trip until the bikes meet and squish your question is how many kilometers did the bee travel in its total back-and-forth trips pause the video and come up with your answer and start it when you're ready to hear what the correct answer is from chapter 1 work we should now realize that if the bikes are 20 kilometers apart and both bikes are moving 10 km per hour they will meet in the middle which means each bike is going to move 10 kilometers traveling 10 km per hour means the bike we'll meet in one hour that means the B only has one hour to live and if the bee is traveling 30 where's per hour it's only going to be out of travel 30 kilometers since it has one hour to live  so the be travel 30 km in a total back-and-forth motion  until it gets squished take a look at quick Quick Chek 2.8 here is a position graph of an object at Keys equal to 1.5 seconds what's the velocity of the object pause the video with needed  the correct here correct answer here is be what we're going to need to do since it's a position versus time graph is fine the velocity at 1.5 seconds right here since it's a long this line we can take the slope of that line segments and the slope will be change my  over run changing X which will give you 20 meters per second in a positive value since it's a positive slope the chicken example 2.3 a train is moving Due West at a constant speed a passenger notes that it takes 10 minutes to travel 12 km how long will it take the train to travel 60 kilometers we might be able to reason this out but I'm going to show you the way we can do it all the work and all the steps while we're giving is that in a time interval of ten minutes that we know that the train can have a change in position of 12 kilometers using our formula that velocity is change in position changing time we can calculate the velocity of the Train by taking 12 km / 10 minutes which would give the train a velocity of 1.2 kilometers per hour if we realize that the trains moving 12 1.2 kilometers per hour and we know it has a change of position of 60 kilometers and I want to know how long that takes will use the same formula velocity is change in position over change in time substituting in our values we have one point two kilometers per hour is equal to our position 60 km overtime and are algebra will tell us that this gives us a Time 5 50 minutes no we're going to take a look at a velocity versus time and find out how we can get the position or the displacement the displacement or Delta X is equal to the area under a velocity versus time graph please note there were analyzing a velocity versus time graph and not a position versus time graph the velocity is 12 at constant 12 meters per second and the Shaded area represents the velocity times time which according to the formula velocity is equal to change in X over  changing time change in X would be velocity times the time let's take a look at Quick Chek 2.11 here is a lacity graph of an object that's at the origin X is equal to 0 at T is equal to 0  at 4 .0 seconds the object's position is what pause the video to collect your answer the correct answer is C 12 M when you have a velocity versus time graph you can find the position play the displacement by taking the area under the line so if we took the area of this segment we would have 4 * 2 8 meters and then if we took the  area under this segment it would have been 1/2 of 4 times 2 which would have given us for  Mater's add those two together in the total area is 12 m from one-dimensional motion an object changing its velocity he is either speeding up or slowing down an object's velocity a speed and direction which is a vector quantity at specific instance of is called the objects instantaneous velocity from now on the word velocity will always mean instantaneous velocity an early time intervals for this graph notice it's a position versus time graph that's curved and in the early intervals the displacement is small therefore the velocity is small as well but in later time intervals it shows that the velocity is increasing and you can remember that in a position versus time graph the slope is equal to the velocity so we can see that the slope is gradually increasing which means that the velocity needs to be increasing as well  in order to get the we would need to actually blow up the small area if I wanted to know the instantaneous velocity on this at that point we would have to blow it up and we can see that if we blow it up enough it looks like a straight line segment instead of a curve and that would be how we would find instantaneous velocity that we won't expect you to blow them up and estimated but you do need to know how to how to interpret a on a position versus time graph let's pause for a minute and look at what the curved lines on a position time graph will tell us in the first situation number one here you can see that you have an increasing pause the slope we can interpret this as since the slope is increasing the object must be speeding up and since it's a positive slope its speed as it moves away from something if you take a look at number to you can also see that the slope is increasing however it's increasing with a negative slope which indicates the object is speeding up but it's speeding up as it's coming back towards something and finally the third one you can take a look and see that you have a decreasing negative slope which means that speed must be decreasing as the object moves back towards the source even when the speed varies we can still use a velocity versus time graph to show the displacement remember area under the curve in any velocity versus time graph equals a displacement even for non uniform motion Quick Check 2.5 the slope at a point on a position versus time graph of an object represents which of the following the correct answer is B if you're looking for the slow the point is going to indicate a velocity at that point and since it's a position versus time graph the slope indicates the when do objects 1 and 2 have the same the law puzzle video with needed  the correct answer is a what is that you have two objects one and two and they're both on position versus time graph which indicates the slope represents the velocity well object is moving at a constant velocity the curved line for object one indicates of the Velocity is changing we need the same velocity we need them to have the same slope so we need to realize that at this location somewhere here object one has very close if not the same slope as object to which occurs sometime before can you was equal to zero masses NQ move with position graph shown do p and Q ever have the same velocity if so at what time or X would this occur  pause video if needed the cut what is a very similar to the previous question although object is moving at a constant velocity we can see that Q very fast and then slows down if we want them to have the same velocity and we're on a position versus time graph we need to we're both of them have the same slope and we can kind of understand that the slope right about there  is this name for p&q so about 2 seconds and finally a car moves along a stretch of road the following graphs show the car's position as a function of time we've indicated several points ABCD and E along this position versus time graph and I like to know at what point or points do the following conditions apply when if ever is the displacement zero  when is the speed zero is the when is the speed increasing and when is the speed decreasing pause the video and get your answers okay at what point is the displacement zero if the position starts here only location D represents a displacement of zero because the object is now back at the starting point when is the speed zero the speed would be zero at points B and since the state can be found by taking the slope of the line on a position versus time graph we would have a zero slope at B and zero slow at e  when is the speed increasing after point a we're going to see that the slope starts to shallow off which me bike that the slope is basically decreasing at that point but I'm sorry this phone is a speed increasing weed B12 increase from the back down to see so at this segment the speed is increasing from B to C and speed is decreasing from a to be we also can Indica indicate that the speed is decreasing along this segment that after you pass D at that point so here we need a little bit more information to get clear that gives you kind of an idea to get started  Mountain class we did start working on a graphing activity but the homework assignment made is on mastering physics site 2.1 through 2.3 hope this video video helped have a great night

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