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If you took a 15 inch artillery shell moving at the velocity it typically goes at, and take that amount of kinetic energy versus the resistive capacity of a sheet of tissue paper, that's the scale that we're looking at here.
如果你有1个15英寸的炮弹,按照经典的速度移动，会消耗大量的动能,抵抗来自于一张薄纸的阻力，这就是我们在这儿看到的尺度。
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In particular, the things that I say are at rest, you will say are moving backwards at the velocity that you have relative to me.
特别是那些在我看来是静止的物体,在你看来却在后退,后退的速度等于我们之间的相对速度
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Let's plot droplet velocity as a function of looking at the number that have this velocity 0 with the zero being in the center here.
我们将液滴的速度设定为,观察那些数字作用，在中心的地方,速度为。
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I would expect, whether you're a Red Sox fan or not, you to be able to look at a list of different pitchers and their average velocity for their fastball, and tell me who has the longest or the shortest wavelength.
无论你是否是一个红袜队球迷，我预想你会看到一系列,不同的投手和他们,投出快球的平均速度，告诉我谁有最长的,或者最短的波长。
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When you're driving in your car, there's a needle and the needle says 60; that's your velocity at this instant.
当你在开车时,有一根指针指着60,表示你这个时刻的速度
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Well, we say at the top of the loop, when it goes up and comes down the velocity is 0.
在曲线顶端,当物体上升,然后速度为0时候
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But things which were at rest will move at a constant velocity, opposite of the velocity that you have relative to me.
这些静止的东西都在匀速运动,方向正好跟你相对我运动的速度方向相反
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This is the starting speed, that's the rate at which it is gaining velocity, and that's how long it's been gaining it.
这是起始时的速度,这是速度的增长速率,这是加速的时间
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What de Broglie is saying we can know the wavelength of any matter at all, as long as we know its mass and it's velocity.
通过德布罗意所说的,只要我们知道了,它的质量和速度，我们可以知道,任何物质的波长。
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That limit will be some arrow we can call the velocity at the time and it will always be tangent to the curve.
那个极限也就是一个矢量,我们称之为瞬时速度,并且它总是和轨迹相切的
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So the velocity at any part of the curve is tangent to the curve at that point.
曲线上任意一点的速度,都在该点和曲线相切
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So the Earth is an inertial frame of reference, if you go in a train relative to the Earth at constant velocity, you're also inertial.
所以,地球是一个惯性参考系,如果你坐在相对于地球匀速运动的火车里,你也处于惯性状态
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You will find that objects that are at constant initial velocity maintain the velocity.
你也会发现原本匀速的物体,依然保持原来的速度
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It's in the nature of things to go at a constant velocity.
能保持恒定速度是物体的固有性质
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It knows that this particle happened to have a height of 15, at the time of 0, and a velocity of 10, and it is falling under gravity with an acceleration of -10.
这个质点恰好处在高度为15的地方,零时刻,初速为10,并在重力作用下以-10的加速度下坠
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What it means is if you'd release a rock at that location one second before with a certain speed that we can calculate, it would've ended up here with precisely the position and velocity it had at the beginning of our experiment.
它的意义在于,若在该处以特定速度抛出一个物体,这个速度可通过计算得到,一秒之后,物体会运动至我们设定的起点,并且速度为我们设定的初速度
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For example, if you started here and you did all this and you came back here, the average velocity would be zero, because you start and end at the same value of x, you get something; 0 divided by time will still be 0.
例如,如果你从这里开始运动,经过这个过程又回到这里,平均速度就是0,因为初态和末态的位移相同,你得到了什么呢,0除以时间还是0
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That is the whole triumph of calculus is to know that by looking at the position now, the position slightly later and taking the ratio and bringing later as close as possible to right now, we define a quantity that we can say is the velocity at this instant.
这就得靠微积分了,通过了解它现在的位置,和一小段时间以后的位置,计算它们的比,再让时间间隔尽可能缩短,我们就定义了一个,被我们称之为瞬时速度的物理量
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At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.
在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度
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If you took the derivative of this, you will get the velocity at time t, it would be: v=v0+at.
如果你对它求导,你就可以知道 t 时刻的速度,即,v=v0+at
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I tell you the initial velocity v0, I tell you at what angle I fire it.
我会告诉你们初速度 v0,以及我以多大角度射出
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But before you even do that, I want to define for you an important concept, which is the velocity at a given time, v .
但在这之前,我要给你们定义一个重要的概念,也就是给定时刻的瞬时速度v
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If you want to know how fast it's moving at a given time, if you want to know the velocity, I just take the derivative of this answer, which is 10-10t.
如果你想知道它在给定时刻的运动有多快,如果你想知道它的速度,我只要对这个式子求导,得到10-10t
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Then, to find the meaning of b, we take one derivative of this, dx/dt, that's velocity as a function of time, and if you took the derivative of this guy, you will find as at+b. That's the velocity of the object.
接下来,为了弄清b的含义,我们取它的一阶导数,dx/dt,得到速度作为时间的函数,如果你对它求导的话,你会得到at+b,这就是物体的速度
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I think you can tell by analogy with what I did in one dimension that the position of that object at any time t is going to be the initial position plus velocity times t plus one half a t square.
你们可以类比一下我在一维情况下的结论,这个物体在任意时刻 t 的位移,等于初始位移,加上 v ? t + 1/2 ? a ? t^2
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