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Khan academy calc 18/9/2023 So divide by five five seconds, that gives us And how long it took him to do that? Well, it took it five seconds. It's traveling in the opposite direction. You see his displacement is negative four. So it's zero minus four which is minus four. Another way to think about it, is that displacement is final position minus the initial position. So what's it's displacement? We might think it's four So we'll call that velocity as VD again, displacement over time. So now let's go ahead and figure it out what it's velocity was. Seconds notice it is back to the starting position. All right, let's see at time zero, where is our dog? Well, it's over here. This dog did in this race? And find out what it's velocity was? I'm pretty sure you can. There was a dog as well, and here is it's position time graph. It turns out there was another competitor in the race. And so at a glance, justīy looking at which one is more steep we can figure out which It kind of makes sense, right? More steep, that means And so this means in a position time graph if something is steeper, that means it has a higher velocity. This is easier to climbīecause it's less steep. Can you see to climb this graph it's a little harderīecause it's more steep. Treated this as mountains and if you were to climb these mountains Let's say you wereĬlimbing these mountains. Can you see that? What I mean to say is if you Also, another important thing you can note is that Nishal who has a higher velocity her graph is steeperĬompared to Mervyn's graph who has a lower velocity. Great idea to go back watch those videos and Spoken a lot about this in previous videos. Graph was not a straight line if it was some kind of a curve like this, then we would see the the Graphs are straight lines it means the position Again, uniform motionīecause it's a straight line. She is constantly traveling every second, three meters first second, three meters. And the same is theĬase for Nishal as well. Graph because the graph is a straight line. And that means his velocity is a constant. Another second, he travels another meter. Second he's traveling one meter first second, he travels one meter. Mervyn's graph one more time what you see is that every Super important to understand that is, if you look at Of course we had already figured that out, but her velocity is And so that will equal six divide by two. Does that make sense? It took her two seconds to do that. She ends at four, but she started at two. To do the displacement? It's not four seconds. So what was her displacement? Again, her displacement So we have to consider this time from two second to four second. Velocity for Nishal would be, again our displacement by time, so she starts over here and she ends the race over here. Nishal's velocity is? Go ahead, give it a try. Again can you give it a try? Can you find out what So he travels at one meters every second. So his displacement was six meters, his time was, time taken for theĭisplacement was six seconds, and so his velocity turns out So, over the six seconds hisĭisplacement was six meters. You can calculate over any time you want, but let's calculate over six seconds. So can you pause for a while and see if you can figure out Mervyn's velocity yourself? Go ahead, pause, give it a try. Velocity for the entire race? Well, how do we calculate velocity? We calculate velocity asĭisplacement over time. So let's see if we can now figure out what were their velocities. In fact, really two seconds, because she came late, to finish the race. To finish the race, she took only four seconds. At four seconds she isĪlready at six meters, she has finished the race. Wow! She is fast! Do you see that? At two seconds she was at zero, at three seconds she'sĪlready at three meters. At three seconds she isĪlready at three meters. Let's see what happensĪt the third second. Where was she at zero? Well, at time zero she's So what we see from his graph is that it took him six At two seconds, he isĪt two meters and so on. At one second, he is over here, at one meter. For example, this is Mervyn's graph, it says that at time zero, he was at zero. What happened at the race, who won the race, and who was faster? So a position-time graph gives us the position of any So let's look at this graph and see if we can figure out See it, so I asked them, "Do you have a recording of it?" And they said, "Yes." So I said, "Good, give it to me." And they gave me this, a position-time graph of what happened. Mervyn and his wife had a race yesterday and I missed it.
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