The answer is that simply knowing the particle has an acceleration is not enough to tell you where the particle will be.

答案是这样的,仅仅知道质点的加速度,是不足以告诉你它接下来的运动的

耶鲁公开课 - 基础物理课程节选

This particle is constantly changing its direction, but it therefore has an acceleration and the acceleration, we have shown here, is pointing towards the center.

这个质点恒定地改变它的运动方向,因此它具有加速度,而且这个加速度,我们前面也讲过了,指向圆心

耶鲁公开课 - 基础物理课程节选

I want to consider a particle which has definite acceleration a, a constant one, but a is now a vector.

我想考虑一个加速度为 a 的质点,加速度恒定,但 a 是一个矢量

耶鲁公开课 - 基础物理课程节选

When a particle moves in a circle, it has an acceleration towards the center of this size, v^2 over R.

当一个质点在圆周上运动时,它有一个指向圆心的加速度,v^2 / R

耶鲁公开课 - 基础物理课程节选

You're only given the particle has acceleration a, and you are asked to find out what is x?

你只知道质点的加速度为a,你需要求出x是多少

耶鲁公开课 - 基础物理课程节选

So what I'm saying here is we are specializing to a limited class of motion where the particle has a definite acceleration, a.

我在这里想说的是,我们正在专门讨论一类问题,这些问题中,质点都有一个确定的加速度a

耶鲁公开课 - 基础物理课程节选

You can easily check by taking two derivatives that this particle does have the acceleration a.

你可以很容易地通过求两次导来验证,这个质点的加速度确实为 a

耶鲁公开课 - 基础物理课程节选

It tells you when a particle moves in a circle, it has an acceleration in a negative R direction, namely directed towards the center.

它告诉你当一个物体在圆周上运动时,它有一个在 -R 方向的加速度,也就是说是直接指向圆心的

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

We said, "Let's take, for the simplest case that we can possibly imagine, namely a particle moving in one dimension along the x-axis with a constant acceleration a.

我们说过,"考虑我们可以想象的最简单的情况,即质点在一维空间运动,沿着 x 轴且保持恒定加速度 a

耶鲁公开课 - 基础物理课程节选

Whenever you see a particle moving in a circle, even if it's at a constant speed, it has an acceleration, v square over r directed towards the center.

只要看到质点做圆周运动,即使是匀速圆周运动,也存在一个加速度,大小为 v^2 / r,方向指向圆心

耶鲁公开课 - 基础物理课程节选

So, this certainly describes a particle whose acceleration is a.

它确实描述了一个加速度为a的质点的运动

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

Conversely, if you get an answer and it doesn't seem to make sense, then you've got to go back and ask, am I violating some of the assumptions, and here you will find the assumption that the particle had that acceleration a is true as long it's freely falling under gravity but not when you hit the ground.

反过来说,如果你得到一个结果,发现似乎是错的,那么你就应该回过头来问问自己,我是不是违反某些前提了,这个模型中,你就发现,只要质点在重力作用下自由下落,质点具有加速度a的前提是正确的,但是落地后就不成立了

耶鲁公开课 - 基础物理课程节选