我来把更一般的形式，写出来吧，在一维空间中，位置和速度，作为时间函数的，一般形式，这里的加速度是一个常数。

I now would like to write down, in most general form the equation for the position and the velocity as a function of time for a one-dimensional motion whereby the acceleration is constant.

youdao

上一课的方程我们，已经比较熟了，常数加速度的，一维运动方程。

We know the equations so well from our last lecture from one-dimensional motion with constant acceleration.

youdao

请注意此处的加速度，是一个常数，不随时间变化而变化，不过速度是变化的。

So notice that the acceleration is constant in time, is not changing but the velocity is changing.

youdao

A limited class of problems is one in which the acceleration is just a constant.

在这类有限的问题里,加速度均为常数

耶鲁公开课 - 基础物理课程节选

So you cannot use the formula once it hits the ground because once it hits the ground, the fundamental premise that a was a constant of -9.8 or -10 is wrong.

当物体落地以后,该公式就不适用了,因为当物体落地后,公式的基本前提——,加速度为常数-9.8或-10——就不成立了

耶鲁公开课 - 基础物理课程节选

take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.

对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r

耶鲁公开课 - 基础物理课程节选