Dependent and Independent Variables

in this video we're going to focus on the dependent variable and the independent variable so first what is the difference between the dependent variable and the independent variable what you need to know is that the independent variable is associated with the xais the dependent variable is associated with the AIS or the variable depends on so the dependent variable depends on the independent variable the independent variable is associated with the experimental group the experimental group is set up as the control group but it differs from the control group in one factor the control group is simply used as comparison but just make sure you know that the dependent variable is associated with the y- AIS and the independent variable is associated with so now how can we apply this information how can we use it in the problem let's try this problem an experiment was designed to measure the net force acted on objects with different masses plot the data shown Below on graph so here we have physics related problem what we need to determine is which one is the dependent variable and which one is the independent variable keep in mind the dependent variable depends on the independent variable so does the force depend upon the mass or does the mass depend on the force in this particular example notice that we can select objects with different masses so we can vary the mass that's something that we have control over so therefore this is the independent variable which is associated with the quantity that we're measuring that's the dependent variable we want to see how the force depends on the mass so therefore Force we should put that on the AIS and we should plot the mass on the xaxis so we're going to adjust these values by 10 on the x-axis and on the axis each Mark will represent 20 so this is about 100 so the first point is at 1020 approximately which is over here then we have another point at around 20 very close to 40 and then 30 80 and finally 50 100 so we have straight line let's do that again now what kind of relationship do we see between the force and the mass is it linear quadratic inverse what type of relationship do we have here so we have linear relationship since we have straight line and so this is proportional or direct relationship we could say that the force varies directly or proportionally with the mass so as the mass increases the force increases now what is the slope of the line notice that the mass increases by 10 and the force increases by 20 the slope is the change in / by the change in it's rise over run so the change in force is about 20 newtons and change in mass is approximately about 10 kilg so we could say the slope is equal to 2 and it turns out that the slope of this graph represents the acceleration of the object which is approximately 2 m/s squ or you can say 2 Newtons per kilogram which is really m/s squ now if you choose any two points you should get slope approximately two may not be exactly two but it rounds to two now you might have seen slope equation like this 2 - y1 over X2 - X1 it's the same as the expression that have here here Y2 - y1 represents the change in X2 - X1 represents the change in so that is it for this question and let's move on to our next example here's another problem feel free to pause the video and see if you can work out this problem as well and then unpause it to check the solutions so an experiment was set up in such way to measure the pressure of gas at different volumes plot the data shown below and determine the relationship between pressure and volume so which one is the dependent variable and which one is the independent variable is volume the dependent variable or the independent variable notice that we want to measure the pressure the quantity that you want to measure is typically the dependent variable so pressure is associated with the variable now we want to measure the pressure at different volumes that means that we can adjust the volume we can put the gas in any container we want we can put it in one lit container two container we can control the volume of the container the quantity that you can manipulate or control that is the independent variable that's so you can adjust the volume to whatever value you want and you want to measure the pressure at that volume so pressure is going to be on the AIS and volume it's going to be on the x-axis so on the AIS I'm going to go by twos so this is going to be 10 ATM and on the x- axis I'm going to go by one so this is going to be 5 lers so the first point is at 1 comma which is somewhere over here the next point is 2 comma 4 or 4 4.1 and then it's three and 2.7 and then we have another 42 and then five 1.6 so we have graph that is decreasing over time so what kind of relationship do we have whenever you have graph that looks like this this is an inverse relationship so as volume increases pressure decreases so we have an inverse relationship graph and that's all we can do for this particular problem here's another problem that you can try another experiment was designed in such way to measure the total distance traveled by an object under Conant acceleration with different time periods plot the data and determine the relationship between distance and time so what's the first thing that we need to do we need to determine which one is the dependent variable and which one is the independent variable so what do we want to measure so in this experiment we wish to to measure the total distance which is the independent variable no take that back that is not the independent variable that's the dependent variable so that's why the quantity that you want to measure it's always the dependent variable and you should put that on the AIS the quantity that you can adjust or that you control that is the independent variable and so that has to go on the xaxis and notice that we measure the distance traveled by the object at different time periods we can measure it in 3 seconds we can measure in 10 seconds we can control the time that we choose to measure the distance now that we've identified the dependent and the independent variable we know where to put the distance and where to put the time so the distance is going to be on the AIS and the time is on the x- axis typically time is usually the independent variable don't think I've ever seen time on the AIS time is usually on the x- axis on the x- axis we're going to go by one until we reach five and on the axis let's go by 20s 20 40 60 80 100 and 120 so the first point that we we have is 1A 5 which is probably somewhere close to the axis and then it's two approximately 20 and then three it's about 45 and then at four it's up to 80 and then at five it's about 125 so notice that this graph it's increasing at an increasing rate so how would you describe the relationship of this graph so what we have here is quadratic relationship or parabolic relationship the relationship between distance and time is associated with this equation so if an object accelerates from rest here's the equation that you need so let's say if we plug in five for the distance and the time is one if you multiply both sides by two you'll see the acceleration is approximately 10 5 * 2 is 10 now if we were to choose different point let's say if we where to use the last Point 125 so using the same equation let's round 24.8 to 125 for the distance and is 5 so 5^ is 25 if we divide both sides by 25 125 ID 25 is 5 so we have 5 is equal to 12 and then if you multiply both sides by two you'll see that is approximately 10 now the slope of distance time graph will give you the speed for displacement time graph the slope represents the velocity and the slope of velocity time graph is the acceleration but the relationship between distance and time you can see that is proportional to t^2 so that's why we could say it's quadratic because the is squared so that is it for this video thanks for watching and have great day