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Displacement from time and velocity example

AP.PHYS:
INT‑3.A (EU)
,
INT‑3.A.1 (EK)
,
INT‑3.A.1.1 (LO)
,
INT‑3.A.1.2 (LO)
,
INT‑3.A.1.3 (LO)
Worked example of calculating displacement from time and velocity. Created by Sal Khan.

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  • aqualine tree style avatar for user varshini.suresh2
    i still dont understand the displacement
    can you help
    (73 votes)
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    • duskpin ultimate style avatar for user Sayan
      The simplest way to remember what is the meaning of displacement is to just remember this phrase- "Displacement is the shortest distance between two points in space."
      To illustrate, imagine a body which travels 4m north and turns right at 90 degrees to the east, and travels 3m. So the shortest distance or DISPLACEMENT is actually the hypotenuse, or 5m. Best of Luck!
      (45 votes)
  • male robot hal style avatar for user Conor McKenzie
    Why is s used for displacement, and not d with a half-arrow over it? How did it come about that we used s instead?
    (14 votes)
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    • spunky sam blue style avatar for user Matthew Bigby
      The answer to this question is calculus. In calculus, Godfrey Wilhelm Leibniz used the notation d/dx to indicate when he was taking a derivative of an equation, as opposed to Isaac Newton who simply used a hash mark. (As it turns out, Leibniz's notation is much simpler to use in calculus when dealing with derivatives and integrals and the like.)
      So, the reason s is used is so that when you start doing calculus in physics, you don't make a confuse the displacement of an object with taking a derivative of an object and get a really bad answer.

      I hope that helped.
      (39 votes)
  • blobby green style avatar for user Taja Nicole Allen
    I was taught that since the answer is "south" it should have a negative and a y-hat symbol. Is that wrong?
    (8 votes)
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    • leafers ultimate style avatar for user GFauxPas
      Maybe you mean j-hat? Sal has videos on that, it's called engineering notation, and it's not wrong. Though actually I don't see any reason why you can't use y-hat, as long as you're consistent throughout the problem. It's just a name, after all.
      (11 votes)
  • duskpin tree style avatar for user STUNNED>
    What's the difference between displacement and distance?
    (5 votes)
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    • leaf yellow style avatar for user Kory
      The first answer was correct, displacement does need a quantity and direction. Displacement can be calculated by measuring the final distance away from a point, and then subtracting the initial distance. Displacement is key when determining velocity (which is also a vector). Velocity = displacement/time whereas speed is distance/time. If I walked to school, then i realized that I forgot my homework and ran back home (all of which took me 20 min. and I live 500 meters away from school), then my average velocity would be 0meters/20min. My average speed on the other-hand would be 1,000meters/20min.
      (14 votes)
  • duskpin ultimate style avatar for user Julie
    Why is it not -300 m? Or is it just 300 m because Sal includes that the direction is to the south? If he didn't mention that the direction is south would it be -300 m?
    (7 votes)
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  • leaf green style avatar for user Sobia Mahmood
    At , Sal cancels out the seconds... How does that work? How come we can cancel out the units? What about the corresponding numbers?
    (3 votes)
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  • purple pi purple style avatar for user juddjasmine
    my teacher talked about m/s/s or m/s2 what does that mean?
    (2 votes)
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    • leaf green style avatar for user knutover
      This is the unit for acceleration.

      You can think of it like this. Speed is the change in distance over time, so its units are meters per second. Acceleration is the change in speed over time, so its units are (meters per second) per second. Written another way it is (m/s)/s = m/s^2.
      (6 votes)
  • aqualine sapling style avatar for user Allécto
    Hello,
    Can I get an example of when "time" is not actually "change in time"? In every problem I can think of, "time" pretty much means "change in time".
    Thanks a lot!
    (4 votes)
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  • mr pants orange style avatar for user Kumar Rajneesh
    if we denote west as (-) and east as (+)
    then what do we denote north and south with .
    the above infor mation was from the video before this one
    solving of time.
    please tell!
    (2 votes)
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    • aqualine ultimate style avatar for user ScienceLover7
      Normally in a problem, you will be given only the forward and backward directions which are opposite to each other. This is One dimensional motion (motion in a straight line). Usually, you will be given only opposite directions.(like east and west, north and south, up and down, etc.) When you are given east and west, you won't have north and south in your problem and vice-versa.
      North, east are normally denoted as positive.
      South, west are normally denoted as negative.
      You usually won't get any problems having north, east or south, west mixed up. Ignore signs in such cases.
      (5 votes)
  • blobby green style avatar for user wolfsea
    At in the video what does he mean by the delta?
    (3 votes)
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    • piceratops ultimate style avatar for user Hecretary Bird
      Delta is a symbol used in math that means "change in". Δt would mean the change in time. This means the difference between an initial time and a final time. However, since it's almost always easier to just think of the initial time as 0, we can replace Δt with just t, which represents the final time.
      Δt = t_f - t_i = t_f - 0 = t
      (3 votes)

Video transcript

Let's do one more example dealing with displacement, velocity, and time. So we have if Marcia travels for 1 minute at 5 meters per second to the south, how much will she be displaced? Let me do it this way. We know that velocity is equal to displacement divided by time. And it's really, once again, it is change in time. But we'll just say time. That's implicitly change in time. And if you manipulate this a little bit, you really just multiply both sides by time. You just multiply both sides by the variable t. You get displacement. Because this cancels out. You get displacement. And I'll flip this around. What's on the right-hand side, I'll write on the left. So you get displacement is equal to time times velocity or velocity times time. Is equal to velocity times time or velocity times change in time. So over here, they're asking us for displacement. They're asking us how much did Marcia get displaced? And they're saying that she travels for 1 minute. So this 1 minute right over here, this is her time. Sometimes you could view that as her change in time. Or it really is her change in time. If it said 0 minutes on her stopwatch when she started, at the end it'll say 1 minute. Or if it said 5 minutes, if maybe it was 3:05 when she started, it would be 3:06 when she finished. So it was really the change in time. Once again, I won't write the delta there just because this is the way you most frequently see it. But I want to tell you that these are the same thing for the purpose of this problem because sometimes you'll see the delta there. So the 1 minute, so the t right over here is 1 minute. At 5 meters per second to the south. This right over here is the velocity. They give us the magnitude, which is 5 meters per second. Or you could say that's the speed. And they also give us the direction, to the south. So this right over here is 5 meters per second to the south. So we might just say, look, if we want displacement, that's just going to be equal to 5 meters per second to the south times 1 minute. The problem here is that when we're talking about displacement, we're going to think about a magnitude of how much it's moved. So it'll be a distance of some kind. And some direction. We have our direction here, but we don't want any other units there. And if we just multiply this over here, we have 1 minute over here. But we have seconds in the denominator. You can't just cancel out a minute and a second. So you can't just say that you're going to get 5 and have some weird thing here. So in order for it to all work out, you have to either convert the 5 meters per second to 5 meters per minute. Or let me phrase that another way. You have to convert the 5 meters per second to some amount of meters per minute, not 5 meters per minute. It's going to be different. Or you convert the 1 minute to seconds. So at least in my mind, it's easier to convert 1 minute to seconds. So let's do that. So this is the same thing. 1 minute times. And we want to get rid of the minute. And the minute is essentially in the numerator right now. We could put this over 1. But it's essentially in the numerator. So we want to divide by minutes. And we want to multiply by seconds. We want seconds in the numerator. And so how many seconds are there per minute? You have 60 seconds for every 1 minute. And so you have a minute cancelling out with the minutes. And so now you have 5 meters per second to the south times 60 seconds. This is now cool because you have seconds and seconds. I wrote "sec" there, but this is also sec. So now you have seconds over seconds. Those cancel out. And so your displacement is going to be equal to 5 times 60. And then your units left are meters. All the time units have cancelled out and then it's meters to the south. So meters to the south. And this is equal to 5 times 60 is 300 meters to the south. And we are done. That's how much she has been displaced. If they just wanted the distance, you could say that she traveled 300 meters. Just that part. The magnitude of the displacement, that is the distance that she traveled.