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He found that some droplets had a certain velocity, and then others had a velocity plus some step.
他发现了一些液滴存在某个速度，还有其他的液滴有速度和位移。
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If the base move is 0, then the price doesn't change So that makes sense. Interesting question.
如果这个基础位移是0，这个价格就不变,这是有道理的吗，很有意思的问题。
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If I gave you the location of a particle as a function of time, you can find the velocity by taking derivatives.
如果我给出物体的位移是时间的函数,你可以通过求导来得到速度
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And he couldn't get values of velocity in between certain steps.
他得不出两个点之间,位移的速度。
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Simply knowing the acceleration is not enough to tell you where it was at the initial time.
仅仅知道加速度是,不足以告诉你它在初始时刻的位移的
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If all you know is the particle is falling under the affect of gravity, that's not enough to say where the particle is, right?
如果你只知道,质点受重力作用下落,那并不足以表明物体的位移,对吧
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Here, we are not talking about a single number, but a displacement in the plane.
我们现在不是在讨论数字,而是平面上的位移
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So the meaning of the constant is where was the object at the initial time.
常数的含义是,物体的初位移
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The question I have is, "What is its location at all future times?"
我的问题是,"它之后的位移是多少"
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They tell you the initial location and initial velocity of the object.
它们表示的是物体的初始位移,和初始速度
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You give me the time and I'll tell you where it is.
给定时间,我就能告诉你它的位移
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Then again, you will find the evolution of the planetary motion, because the rate of change of the rate of the change of the position is connected to the position.
同样地,这就是行星运动的演化过程,因为行星位移的变化率的变化率,与它的位移有关
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For that purpose, to describe that displacement, we use a vector.
在这种情况下,我们就用矢量来描述位移
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You get to pick where it was at the initial time.
你需要选取初始时刻的位移
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The acceleration gives you an extra stuff, quadratic in time.
加速度对位移有额外贡献,是时间的二次项
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When does it hit the ground" is "When is y=0"?
何时落地"也就是"何时位移为零"
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Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.
只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数
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C indeed represents an effective displacement.
其实表示的是实际位移
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Even though we started with a single vector, which is the position vector, we're now finding out that its derivative has to be a vector and the derivative of the derivative is also a vector.
即使我们从单个矢量出发,即位移矢量,我们现在也能得出它的导数是矢量,而且导数的导数也是一个矢量
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You need three positional measurements.
你需要测量三次位移
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It's got an initial position.
它有一个初始位移
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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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Initially, its location as a function of time is equal to i times x plus j times y.
初始时刻,它的位移作为时间的函数等于,i ? x + j ? y
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So I realize that the constant, c, is the initial location of the object, and it's very common to denote that by x0.
所以我发现常数c,就是物体的初位移,我们习惯用x0表示
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The answer was: at any time t, the location of the particle is given by this formula.
答案是,在任意时刻 t,这个质点的位移都由这个式子给出
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Then for any time t, you plug in the time t and you will get the location.
那么在任何时刻 t,当你代入 t 的值,就可以确定位移
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Consequently, for this object the position y, at any time t is known to be 15+10t-5t^.
因此,对这个物体来说,在任意时刻的位移y,就应该为15+10t-5t^
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So, this is the most general position for a particle of constant acceleration, a.
这是一个加速度为a的匀加速质点,位移的最一般的表达式
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So, the question we are going to ask is the following, "If I tell you that a particle has a constant acceleration a, can you tell me what the position x is?"
接下来要问的问题就是,如果我说某质点加速度恒为a,你能告诉我它的位移x是多少吗
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Then, in every situation where the body has an acceleration a, the location has to have this form, where this number is where it was initially, this was the initial velocity of the object.
在任何研究对象具有加速度a的情况下,它的位移就一定具有这种形式,这个系数代表了它的初位移,这个代表了它的初速度
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