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

耶鲁公开课 - 基础物理课程节选

You get to pick where it was at the initial time.

你需要选取初始时刻的位移

耶鲁公开课 - 基础物理课程节选

One is initially. We are not interested in that.

一个是初始时刻,我们对它没兴趣

耶鲁公开课 - 基础物理课程节选

By "Present," We mean-- we will pick some part of the universe we want to study and we will ask, "What information do I need to know for that system at the initial time, like, right now, in order to be able to predict the future?"

我们所说的"现在",意思是,我们会选取客观世界某一部分来进行研究,然后我们就会问,我们需要什么信息去了解,初始时刻的系统,比如现在,进而能使我们能够预测未来呢

耶鲁公开课 - 基础物理课程节选

So，the point is,every object falling under gravity is given by the same formula, but there are many, many objects that can have many histories, all falling under gravity, and what's different from one object and the other object is, when was it dropped, from what height, and with what initial speed.

关键是,每一个受重力作用下落的物体,都有同样的表达式,但是各个受重力作用下落的物体,都有不同的初始条件,所以它们的区别在于,下落时刻,下落高度和初始速度

耶鲁公开课 - 基础物理课程节选

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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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

耶鲁公开课 - 基础物理课程节选