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.

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。

youdao

So, if you just look at the position vector, and the velocity vector for any motion at any given time, then together, they determine some plane.

如果你看一下任何时刻运动时的，位置矢量和速度矢量，它们决定了某个平面。

youdao

And, the way we can get it, so, it's called usually V, so, V here stands for velocity more than for vector. And, you just get it by taking the derivative of a position vector with respect to time.

根据它的原理，我们通常用v表示,这里的V更代表速率而不是矢量，你能通过,对一个关于时间的位置向量求导得到它。

youdao