It is interesting for him to study the derivative of a vector.

对他来说，研究矢量的导数是很有趣的事。

youdao

So, the definition will take effect. The acceleration is as a vector, and the acceleration vector is just the derivative of a velocity vector.

有必要对加速度给出一个严格的定义，加速度,作为一个矢量,是速度的一阶导数。

youdao

So, the velocity vector is the derivative of a position vector with respect to time.

速度向量，是位置向量关于时间的导数。

youdao

Why is the derivative of a vector also a vector?

为什么矢量的导数还是一个矢量呢

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

You can take a derivative of the derivative and you can get the acceleration vector, will be d^2r over dt^2, and you can also write it as dv over dt.

你可以对导数再求一次导,你就可以得到加速度矢量,也就是 d^2 r / dt^2,你也可以写成 dv / dt

耶鲁公开课 - 基础物理课程节选