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Video Lesson 2.4 - 2.6

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hello AP Physics today we're going to discuss sections 2.4 through 2.6 of your textbook we watch the free lecture video Excel rhaetian in class you can view this video at the mastering physics website  we're now going to define a new motion to describe an object whose velocity is changing this term is called acceleration the ratio of change in velocity to change time is known as the rate of change of velocity or acceleration  this ratio of change in velocity divided by Egypt time is also the slope of a velocity versus time graph recall that if you have a velocity versus time did the slope  is always changing the Y divided by changing the X but for this graph what's your measuring on the y-axis is velocity and what's your measuring on the x-axis is time and we say this we see that this the same ratio as above so when we take the slope of a line  on a velocity versus time graph that gives us the duration we now need to also give a unit for acceleration  and the common unit for acceleration will be meters per second squared also want to let you know that there is a class video made by one of the authors of your textbook on page 39 of your text I encourage you to take a look at that video then we're going to see we can graph or find an acceleration graph acceleration versus time from analyzing a velocity versus time recall that the slope of a velocity versus time graph is going to give us the acceleration so during this first segment on the velocity versus time graph we will see that the slope is constant so this is going to give us a constant rayshun all the acceleration versus time graph if you would have calculated the slope of that first at segments it would of course bonded to the value shows of the y-axis of your acceleration versus time graph  the second segment on your velocity versus time graph shows a constant how to eat with zero slope so we would represent a constant acceleration of 0 as such on our acceleration versus time craft the last segment on your velocity versus time graph indicates a negative slope therefore it means we have a new acceleration and we wanted to indicate a negative acceleration on the negative side of your acceleration versus time an object can move right or left or up or down while either speeding up or slowing down whether or not an object that is slowing down has a negative acceleration depends on the direction the motion and easy way to remember this is in chart form if we take a look at velocity and acceleration we should recall that they're both vectors in we indicate the direction of a vector with a positive or A negative so if I have a positive velocity and a positive acceleration I'm telling you that both of those vectors are pointing in the same direction just like a negative velocity and a negative acceleration those are also both pointing in the same direction playtime did both your velocity and your acceleration vectors point in the same direction your object has to be speeding up but if you have a positive velocity and negative acceleration or a negative acceleration  and I are thinking of a lawsuit acceleration that represent that they are both in the opposite direction and your object has to be slowing down so what does a negative acceleration doesn't indicate the object is slowing down you have to look at the signs or the both the velocity and the acceleration vector in order to determine if an object is speeding up or slowing down the list look at the pictures that are shown if you take a look at the first  picture the tear from the motion diagram we can see that the object speeding up but why it's speeding up is because the velocity vector and the acceleration vector are both pointing towards the right we both would have been positive looking at the corresponding velocity versus time graph we can see that the velocity is because it's in the  top quadrant and since the acceleration is the slope of a line on a velocity versus time graph the is also positive since it has a positive slope so when you have a positive velocity and a positive acceleration your object has to be speeding up take a look at the second picture from our motion diagram at the top we can see that the velocity vectors pointing to the left while the acceleration vector is pointing to the right that should indicate that the object is slowing down and you can see that in the are the velocity vectors that are shown but now take a look at the graph from the graph we see that there is a negative velocity because stop the negative section of the graph but this slope is positive  which means the acceleration must be POS if you have a positive acceleration and a negative velocity your object has to be slowing down  the third situation from our motion diagram we can see that the velocity is moving to the right while the acceleration is moving to the left so they should indicate that your object is slowing down which you see in your motion diagram but now take a look at the graph your velocity is positive because it's all dup top part of your graph but the acceleration has to be negative because the acceleration is represented by the slope of the when the slope is negative again here the graph even represents a positive velocity in a negative acceleration which indicates the object is slowing down it finally situation number for for the motion diagram we can see that the velocity is to the left the acceleration is to the left if they're both pointing in the same direction the object must be speeding up from the graph this is also indicated with negative velocity and a negative acceleration because the slope was negative both have the same signs so it has to be speed it up remember you have to take a look at both the direction of the velocity and the acceleration to determine whether the object speeding up or slowing down  let's take a look at a video burn animation  notice while the object is going down the incline The Ville Steve actor is getting bigger which means it's speeding up this is because the velocity and acceleration vectors both point in the same erection  but after the curve you should notice that the velocity Vector is getting smaller which means it's slowing down cheer the velocity and acceleration vectors are in opposite directions we'll talk about the curved section in a later chapter let's take a minute and do a quick check the a particle has a velocity of V1 as it moves from .1 to .2 Eurasian is shown what is the velocity Vector V2 as it moves away from .2  please pause video if you need to take a moment to get your answer the correct answer sorry about that the correct answer is fee we can see from the picture that are Velocity Vector is pointing down but acceleration vector is pointing up when that happens the object has to be slowing down so my velocity to Vector needs to be a little bit shorter it's still needs to be pointing down just shorter than V1 another quick check the motion diagram shows a particle that is slowing down the sign of the position X the side of the Velocity are which of the following take a moment start the video when Eddie  the correct answer here  is B  to determine the direction of the position you first have to look at the origin and notice that are motion is taking place to the right of the origin which indicates a position what is positive but the velocity vectors are pointing to the left which would indicate a negative velocity if this question asked the direction of the acceleration is you would have said it was positive  there are four motion diagrams the show the motion of a particle along the x-axis which motion diagrams correspond to a positive Excel which motion diagrams correspond to a negative acceleration and get your answers in diagram a we're going to see that it represents a positive acceleration this is because you can see the velocity vectors are getting bigger as it from the left to the right since the velocity vectors are getting bigger it's indicating the object is speeding up so if you have a velocity Vector that is positive only way then object can speed up is if the acceleration vector is also positive  if you take a look at diagram motion diagram this is going to represent a negative  acceleration  since the starting point is at the beginning in this motion die we have a positive acceleration but from the motion diagram we can see that the object must be slowing down and that would require an Excel rhaetian that has the opposite sign or negative motion diagram C shows a positive acceleration since the velocity vectors are pointing to the left you would have a negative velocity the velocity vectors are decreasing so that indicates the object is slowing down which means the acceleration has to be opposite of the velocity can finally D has a negative  acceleration since the start is on the light and we see that the velocity vectors are moving to the left we have a negative velocity and the motion diagram show that the object is speeding up so in fruit to speed up your acceleration have to point in the same direction which gives you a negative acceleration checkpoint 2.18 bike jumps out of a tree and lands on a trampoline the trampoline sags 2ft before launch bike back into the air at the very bottom where the SAG is the greatest what is Mike's acceleration the acceleration would be Upward at this point Mike is changes Direction and if Mike's about to launched up you would have to be enough direction another way you can think about this is that Mike's motion was down his below he was down when he was jumping and since he was slowing down to a stop his acceleration would have to have been in the opposite direction as the velocity a cart slow down while moving away from the origin what does the position and velocity grass look like  pause the video if you need some time to get your answer the correct answer is d or these two graphs since the cart is slowing down while moving away from origin we see that the origin is located here in so it's to the right of the origins our position versus time graph needs to be graphed what's a positive displacement also the slope of a Velociraptor Scooby the slope of a position versus time graph is going to represent the Ville and since the velocity is decreasing our slope needs to decrease in the positive direction and if you're slow decreasing your velocity versus time graph needs to represent a decreasing velocity in the positive direction which is represented by d  a cart speeds up while moving away from the origin what do the velocity acceleration graphs look like Falls of the video get your answer  hear the correct answer is B or these two graphs if the car is speeding up while moving away this is represented with an increasing positive velocity on the velocity Todd Graff but since the slope of a velocity versus time graph is acceleration we see it should have a constant acceleration which is represented velocity  or something all the acceleration versus time graph here is a motion diagram of a car speeding up on a straight road what is the sign of the acceleration good answer is B negative this is similar to the earlier quick checks and since the velocity is moving to the left play negative velocity the motion diagram shows that it's speeding up which means your acceleration has to be in the same direction which would have been negative which velocity versus time graph goes with this acceleration graph hear the correct answer is he taking a look at your acceleration versus time graph we first see do you have a negative acceleration for the first segment and on your velocity versus time graph you would have needed your first segment to a negative slope that knocks out a which has zero slope now be still has a negative slope she is knocked out because that's a positive and so is Dee so now we have left b-and-e but the second segment represents a positive acceleration which would mean the second segment of my velocity versus time graph would have to represent a positive slope which knocks out be the slope for the first is negative for your velocity versus time in the second segment was pot which is positive is the only velocity versus time graph that correctly your acceleration versus time graph promotion with constant acceleration we see that we have three formulas the first Formula shows it can be used when the velocity is changing steadily and the second shows the position changes as the square of the time changes and the 3rd we can also Express the change in velocity in terms of distance not time you need to take look at your green AP formula chart and find these formulas there and reference them when you are doing your homework  let's do an example as you drive in your car at 15 meters per second that's just a bit under 35 miles per hour you see a child fall go into the street ahead of you you hit the brakes and stop as quickly as you can in this case you come to rest in 1.5 seconds how far does your car travel as you break to a stop the first step is going to be to take the information out of the problem they were dry a car with an initial or V1 velocity of 15 meters per second we also noticed that the car comes to arrest so our final or second velocity will be 0 meters per second and it takes a time of 1.5 seconds for this to occur  stop it asked how far does our car travel start unknown is going to be our displacement or change in X  looking back at our three previous acceleration formulas you will see that the formula V2 Square is equal to V 1 squared plus 2 AD should help us solve our equation but we're also missing fix up deceleration or the acceleration of the car is so we also need to find an unknown acceleration before we can proceed get to our final equation a second equation that would help us find the acceleration would be V2 is equal to V1 Plus at substituting in from our earlier earlier values we can see Zero is equal to 15 meters per second plus my unknown acceleration times time which is 1.5 seconds we complete this math we will see that we have an acceleration of 10 meters per second squared now that gives us enough information to plug in to our final equation which is shown here our final velocity was 020 squared is equal to initial velocity was 15 meters per second squared plus two times are acceleration we just what was 10 meters per second squared times are displacement or change in x  after doing will see that our displacement we're changing X comes out as 11.25 meters according to significant figures rounded this to 11 meters for our final answer when you're doing problem solving activities in this class did some strategies that you might want to use you can find in a table in your book jobs involving constant acceleration speeding up slowing down vertical motion horizontal motion can all be treated with the same problem solving strategies make sure you prepare for the problem by drawing a visual overview of the problem this should include a motion diagram a pictorial representation a list of values a graphical representation may also be used for certain problems then we're going to need to solve the problem which is the math solution based on the three equations that were given earlier  the equations are phrased in the terms of the variable X is customary in your textbook to use why for the motion in the vertical direction that you don't have to do this you can use x for horizontal or vertical mode you want to use the equation the best matches what you know and what you need to find for example if you know acceleration and time hair looking for a change of velocity the first equation given would have been the best one and then remember uniform motion that has a velocity will have an acceleration of 0 after you're finished you need to assess it and look and see if your answer or your results believable does it have the proper units and does it make sense one more problem it will be finished it is says a Saturn 5 rocket is launched straight up with a constant acceleration of 18 m per second squared after 150 seconds how fast is a rocket moving and how far has it traveled  we first want to take the information out of the pro and the acceleration is 18 meters per second squared and it was given as a directed we also know that the change in time is 150 seconds they asked how craft is the rocket movie which is going to be our second velocity as well as what was how far it traveled which would have been our displacement  but looking we have to realize that the rocket was launched so we know that V1 was also zero sometimes that's the hardest information to figure out is what is implied by the problem so if we want to find V2 how fast the rocket was moving  an equation that would work for that was V2 is equal to be 1 + 80 all of the known values are given with the exception of the two so we can plug our values in D2 as our unknown is 0 the acceleration was 18 meters per second squared and I'm going to make the direction up positive and our time 100 50 seconds  so after the map we find out that the speed is 2700 m per second which is pretty quick now how far has this gone now we're looking for our displacement which is a different formula and change in X we found by the initial velocity times time plus 1/2 t-squared  substituting in the initial velocity is zero X the time of 150 seconds plus what app the acceleration was 18 meters per second squared times of time 150 seconds don't forget to square according to the formula and are displacement comes out  2.0 top 10 to the 5th meters which is about 126 miles the Saturn 5 rocket when a turn 26 miles in 150 seconds represent pretty quick  travel sections 2.4 through 2.6 younower assigned a homework in mastering physics and I do want you to pay attention that number 3 I'm on the mastering physics is worth extra credit  hope this video is helped hope you have a great night bye

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Video Lesson 2.4 - 2.6

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