Intro to Position-Time Graphs & Velocity

by Patrick Ford
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Hey, guys. So sometimes in your problems you're gonna be given graphs instead of numbers. So in this video, we're to talk about position time graphs and how we use them to calculate things like velocity. Let's check it out now, guys, the basic idea is that a position time graph just shows Ewan objects position in the Y axis. So right here versus time inthe e x axis over here. So right off the bat, That might be kind of confusing because we're gonna use position, which is given by the variable X, but it's actually in the Y axis or the vertical axis. So don't let that confuse you. Make sure you understand that. Now what position time graphs do is they help us sort of understand or visualized the motion of an object much more simply, for example, let's say you wanna walk 6 m forward in three seconds, you stop and then you run 6 m back. So you have to basically draw all the points A B, C D. Label, all the parts and things like that. So we can do is we can actually take this complicated diagram. We could actually represent it much more simply on this graph Here, for example, if you were to go 6 m forward in three seconds on the position time graph, you're going from zero all the way up to six and then in three seconds. So you basically just go up and over six and then three. So you're gonna end up right over here, and then we just connect where you started, from which is at the origin and with just with a straight line like this now, finally are. The second part is that you could have stopped for one second. So basically, from B to C, you actually haven't moved anywhere. It's hard to see on the diagram what's actually happening. But from 3 to 4, if you're not moving anywhere, then your position just stays the same. You started six and you stay at six. So that means we're just gonna connect these points with a straight line. And then finally, you're gonna go from four seconds all the way back to five. And so that just means from 4 to 5 over here, you're going all the way back to where you started from, so that we can label the pieces here A B C indeed. So this graph here just represents everything you did on this diagram, but all kind of just in one place without having to draw all these little things here. And it kind of looks weird. So what The position time graphs also dio is we can calculate the velocity directly from the graph. For example, we know that the the equation is Delta X over Delta T. So, for instance, if I look at the interval from A to B, this little line here, I can actually break this up into a triangle, and I can take a look at the legs of the triangle the legs of this triangle. The vertical piece over here actually represents my change in position because that's on the vertical axis. So you can think about this as like the rise of the graph and the horizontal section, the horizontal leg is delta T. That's the change in time. And you can think about this as the run of the graph. So that means that my Delta X over Delta t on this graph is really just the rise over the run. And that's a phrase we've seen before. it's the slope. So, guys, the velocity is the slope of the position graph. And there's a couple things you wanna know when you have upward slopes like we did from A to B. That just means that you're moving forward. And that makes sense because that represents this motion. Here we move forward. If you have a horizontal slope basically a flat one like this, then that means that you stopped because your position isn't changing. And then finally, a downward slope like this from C to D is when you're moving backwards. Like just We were like Like we're moving in that last section over here, guys, that's all you need to know. Basically, there's just one simple equation. We're looking at a bunch of slopes, calculating some slopes. So let's just get to an example. So you've got this position time graph here. I'm going to calculate the average velocities for these parts. Let's check it out. So we're gonna go from 0 to 2 seconds. All you have to do is just go from 0 to 2, and we just need to identify those points on the graph. So zero, I'm over here and it's too I'm over here and I'm just gonna calculate the slope of this line. So let's go ahead and do that. My average velocity is just Delta X over Delta T. So on the graph, I'm gonna go. I'm gonna I'm gonna end to 10. But I'm gonna start at negative 10. So that means that the Delta X is my final position, which is 10 minus my initial position, which is negative. 10. So this is my final Sorry. That's my initial. That's my final. And so my Delta X is just equal to 20. So I've got 20 and then the time is just from 0 to 2 seconds, so that's just too So that means just to get a positive 10 m per second for the velocity here. All right, let's move on. So the second part is gonna be from T equals two t equals for same thing. We're just gonna go from t equals to two t equals for the lines already drawn for us. Now we just have to calculate the slope. So my average velocity here is just gonna be Delta X over Delta T. So what's the rise? Well, if you notice here we've got a flat line. So that means that the rises zero you actually haven't moved anywhere. You started off a 10 and you ended up a 10. So you haven't actually moved anywhere. There's no rise. So that means that zero over. Whatever the time is in this case, Delta T equals two seconds Doesn't matter because you're still gonna end up with a velocity of zero. And that makes sense because 0 m per second means that you should have a horizontal or a flat slope like this on Ben. You know, when we got 10 m per second, we actually just got an upward slopes. That also makes sense. Now, for the last one, Teak was 4 to 5. So this is just gonna be this section right here from T equals 45 So my Delta X, my rise is gonna be while I'm going from 10. And I'm gonna end up at five. So that means that my final is actually five, my initials 10. Which means that my Delta X is actually negative five. And so the run, my delta t is just one. So that means to calculate my average velocity. My delta X over Delta T is just gonna be negative. 5/1, and that's negative. 5 m per second. And so that makes sense. I got a negative number because it's a downward slope. So everything checks out there now for the last one. What's the velocity for the entire motion? What does that mean? What? We went from 0 to 2 to four and then 4 to 5. So that means for the entire motion. That just means T equals zero all the way to five seconds. So we just identify what's the graphic T equals zero. It's right here in the beginning. What's the gravity equals five. It's all the way here at the end. And the velocity, the average velocity is just gonna be the slope of the line that connects those points. So basically, we could just draw a straight line here, and this slope here is gonna be the average velocity. So that means that you can get the average velocity between any two points on the graph. They don't necessarily have to be connected as long as you can figure out Delta X Delta T. So we're gonna do that so the average equals Delta X for the whole thing over Delta T. So let's take a look. We could make a triangle like this, My Delta X. Well, let's see my final positions. Five. My initial position is negative. 10. So five minus negative 10 and we get 15 and then for the run. Basically, the leg of this triangle here might delta t is just five seconds. So that means that my Delta X over Delta T is 15/5 and that is 3 m per second. And that's the slope. So the last point that you need to know here is that the steepness, or basically how vertical the slope is, has some significance on the velocity. For example, steeper slopes means that the velocity will have a higher magnitude, whereas flatter slopes means that a velocity whoops flatter slopes means that the velocity has a lower magnitude. For example, we had this one velocity here that was 10 m per second, that basically the first section here, and it's more vertical than the average velocity that we calculated over here, which was the 3 m per second at the end. So basically, how vertical, How close to vertical it is will depend what we'll we'll make the number higher on. Basically, the direction is just controlled by whether it's going upwards or downwards. That's it, guys, let me know if you have any questions.