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  • Hi, I’m Dr. Shini Somara and I hear you want to learn physics.

  • I have to say: good choice.

  • Physics is the science of how the world -- really the whole universe -- works.

  • And I don’t know if youve noticed, but in the world I live in, things tend to move around a lot.

  • So that’s what were going to study first: the science of motion.

  • And it turns out to be incredibly useful -- for figuring out things like where you are, or

  • where youve been, or how youre moving through the world.

  • Why is that worth knowing?

  • Well, for one thing: The police use physics to decide how exactly how fast youre moving

  • through the world, and if that motion happens to break the law.

  • So if youre gonna understand how and why you got that ticket they gave you -- and maybe

  • even know enough to dispute it -- you have to know the science of motion, too.

  • And in order to do that, youll need to understand a few essential conditions that

  • describe your physical place in the universe.

  • Conditions like time, position, velocity, and acceleration.

  • So to talk about all of these things at the same time,

  • youll need a set of equations that links all of them together.

  • These are called the kinematic equations.

  • So, for the next few minutes, let’s talk about how you can figure out your place in

  • the world -- literally -- which just might help you beat that speeding ticket.

  • [Theme Music]

  • Let’s say youre driving on a straight stretch of highway. Say, someplace nice and flat,

  • on the wide open spaces of the Northern Plains of the United States. SayNorth Dakota.

  • You come across a red light, and even though there are no cars in sight, you stop.

  • Because youre a good driver who obeys traffic laws.

  • Then, the light turns green, so you hit the gas. Annnnd exactly seven seconds later,

  • you hear the sirens and see the flashing lights of a police car.

  • Youre promptly served with a ticket for speeding in a 100 kilometer an hour zone.

  • But wait. Were you really going that fast? Did you actually break the law?

  • You can’t really tell, because the speedometer in your car is broken.

  • So you need to find another way to figure out how fast you were going, and decide if

  • you want to take this up this issue with Johnny Law in court.

  • That’s where physics comes in -- the physics of moving in a straight line.

  • Let’s start by talking about how your car was moving.

  • Driving along a straight highway is an example of one-dimensional motion because the car

  • can only move back and forth along that line.

  • That’s different from something that’s free to move in all three dimensions,

  • like a boomerang flying through the air.

  • And instead of describing that motion just in terms of speed, or direction, like a police

  • officer or other non-physicist might do, we physicists describe it with math.

  • Maths that measures the four main conditions of the car’s movement --

  • its time, position, velocity, and acceleration.

  • Time simply tells you how long you were driving for. Position is also important: It lets you

  • know where you are or where you were. It can even be negative.

  • For one-dimensional motion, there are only two directions you can move in --

  • in this case, forward or backward, east or west.

  • So, if the change in position -- known as displacement -- is positive, youll know

  • youve moved in one of those directions. If it’s negative, youre traveling the other way.

  • But which direction is positive, and which is negative? That’s totally arbitrary.

  • You could decide that east should be positive and west negative, or the other way around

  • -- but the answers you get will mean the same thing.

  • You just have to make sure to keep track of which direction is positive, and keep that

  • in mind when youre talking about velocity and acceleration, too.

  • Velocity is the way your position changes over time, and it’s also a pretty big deal.

  • It’s kind of like speed, but just like with displacement, it also tells you which direction

  • youre moving in, based on whether it’s positive or negative.

  • Now, what about when your velocity changes?

  • That’s the fourth quality of movement youll want to pay attention to: acceleration.

  • If youve ever been in a car when someone slammed on the gas, that feeling of being

  • pressed back against your seat is acceleration -- your velocity’s changing.

  • So, how do we plot out all of these different conditions that describe the movement of you

  • and your vehicle through the plains of North Dakota?

  • A non-physicist might visualize this movement on something like a map, but for us, graphs

  • are the most useful way to show how all this change in position is happening.

  • Graphs are generally presented as position versus time -- with position on the vertical

  • axis, and time on the horizontal axis.

  • Well label your position as x and time as t.

  • Now, let’s imagine three different scenarios for how you drove through this small town, and graph each one.

  • First, let’s say that, after you went through the red light, you just stayed in one spot

  • -- say, at 4 meters from the light -- for three seconds.

  • From that moment, the graph of your position would just be a flat line at x = 4 m, like this.

  • Now, what if you didn’t stop, but instead were coasting at one meter per second?

  • Then the line would be diagonal, to show how your position was changing -- like this.

  • And the third time, let’s say you were standing still at first at the 4 meter mark, but then you hit the gas,

  • and you moved in such a way that, after 1 second, you went 1 meter in the positive

  • direction and after 2 seconds you went 4 meters and after 3 seconds youve gone 9 meters.

  • In that case, you end up with a graph that’s all curvy, like this.

  • But there’s more going on in these scenarios than just your position and time.

  • You also have to be able to graph your velocity and acceleration.

  • So, to graph your velocity, you’d put your velocity on the vertical axis and time on the horizontal axis.

  • And youll note that, since velocity is measured as the change in position over time,

  • it’s measured in meters per second.

  • The graph for acceleration is quite similar -- acceleration, a, goes on the vertical, and time goes on the horizontal.

  • And since acceleration is measured as the change in meters per second, its units are

  • meters per second per second -- otherwise known as meters per second, squared.

  • So: time, position, velocity, and acceleration all relate to each other.

  • Velocity is the change in position over time, and acceleration is the change in velocity over time.

  • And often, your velocity will be different from moment to moment -- like the third time

  • you drove down the highway, when you hit the gas.

  • But let’s say you wanted to know your average velocity for a certain period -- say, for those first three seconds.

  • All you have to do is take the change in position and divide it by the change in time.

  • Figuring out how much something is changing just means that you have to subtract its starting value from its final value.

  • And since, as physicists, well end up doing that a lot, we abbreviate that difference

  • using the lowercase Greek letter delta.

  • So we can use that to write the equation for average velocity: It’s just delta x over delta t.

  • The change in position over the change in time.

  • Now what about the third scenario? When you had your foot on the gas and kept accelerating?

  • You started out at the 4 meter mark, and ended up at the 13 meter mark. So your change in

  • position, or delta-x, would be 13 minus 4, or 9 meters.

  • And you started at 0 seconds and ended at 3 seconds, meaning that your delta-t was 3 seconds.

  • Over 3 seconds, you moved 9 meters. That’s 3 meters per second!

  • The equation we use to describe average acceleration is a lot like the one for average velocity,

  • because it’s just the change in velocity divided by the change in time.

  • So, in that case, your equation would be delta v over delta t.

  • And! Here’s something that is incredibly handy.

  • Since were talking about constant accelerationthat is, acceleration that takes place

  • at a constant ratewe can rearrange this equation to get v = v_0 + at.

  • That's average velocity equaling to velocity at time 0 plus the product of acceleration times time.

  • This, my fellow physicists, is an equation well be using a lot.

  • We call it the definition of acceleration -- because that’s exactly what it is.

  • It’s saying that constant acceleration is equal to the change in velocity divided by the change in time --

  • we just used algebra to move the variables around.

  • Now, it’s worth noting that there are lots of different kinds of acceleration,

  • ones that don’t involve speeding tickets -- like when something is falling.

  • The force of gravity pulling it down is making it accelerate at 9.81 meters per second squared,

  • which physicists often abbreviate as a lowercase g.

  • So well just call that constant small g … there’s a capital G that’s going to come up later.

  • So, the definition of acceleration is the first of the two main kinematic equations

  • that well be using. But it only links velocity, acceleration, and time. What about position?

  • There’s an equation for that too -- the second kinematic equation, which well call

  • the displacement curve, because it takes your acceleration, your starting velocity, and

  • how long you were moving for, and uses that information to figure out what your displacement was.

  • And the displacement curve equation looks like this.

  • It makes sense, if you think about it -- if your acceleration is the change in your velocity,

  • and your velocity is the change in your position, then there should be some way to link all of them together.

  • Now, there are lots of other kinematic equations, too, like these.

  • But, you only really need to know the first two -- the definition of acceleration and

  • the displacement curve. The others are just different ways of rearranging these main two.

  • And because these two equations have so many terms in common, you can use them together really easily.

  • For example, if you know your acceleration, and your starting and final velocities,

  • you could use the definition of acceleration to figure out how much time you were traveling for.

  • Then you could plug that value for time into the displacement curve equation and use it to find your displacement.

  • Now that we know what the kinematic equations are, we can finally use the power of physics

  • to find out whether you were speeding when the cops pulled you over.

  • As with most physics problems, the first thing we need to do is write down everything we know.

  • In this case, we know your initial velocity, v-nought, was 0, and your time, t, was 7 seconds.

  • The first thing we need to find is your acceleration, which we can get using the displacement curve.

  • Plugging in everything we know, we find that your acceleration, a, was 5 meters per second squared.

  • Then, we can plug all of that into the definition of acceleration, to find your final velocity, like this:

  • We learn that you were going 35 meters per second when the cops pulled you over.

  • That’s 126 kilometers an hourSo you definitely deserve that ticket. Sorry.

  • But, in this very first episode of Crash Course Physics, you learned all about position, velocity, and acceleration.

  • We also talked about the two main kinematic equations:

  • the definition of acceleration, and the displacement curve.

  • Crash Course Physics is produced in association with PBS Digital Studios. You can head over

  • to their channel to check out amazing shows like Deep Look, The Good Stuff, and PBS Space Time.

  • This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio

  • with the help of these amazing people and our Graphics Team is Thought Cafe.

Hi, I’m Dr. Shini Somara and I hear you want to learn physics.

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B1 CrashCourse acceleration velocity position displacement equation

Motion in a Straight Line: Crash Course Physics #1

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    羅紹桀 posted on 2016/04/25
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