But de Broglie has told us that the wavelength is related to the instant velocity through this formula.

但德布罗意曾说过,波长是和瞬时速度相联系的,通过这个公式。

麻省理工公开课 - 固态化学导论课程节选

And this is just a Newtonian expression of momentum, the product of the mass of the electron times its instant velocity.

这只是牛顿学上关于动量的表达，用电子质量,乘以瞬时速度。

麻省理工公开课 - 固态化学导论课程节选

That limit will be some arrow we can call the velocity at the time and it will always be tangent to the curve.

那个极限也就是一个矢量,我们称之为瞬时速度,并且它总是和轨迹相切的

耶鲁公开课 - 基础物理课程节选

The tangent's pointing towards the direction you are headed at that instant.

切线的方向就是,速度矢量在那个瞬时的指向

耶鲁公开课 - 基础物理课程节选

That is the whole triumph of calculus is to know that by looking at the position now, the position slightly later and taking the ratio and bringing later as close as possible to right now, we define a quantity that we can say is the velocity at this instant.

这就得靠微积分了,通过了解它现在的位置,和一小段时间以后的位置,计算它们的比,再让时间间隔尽可能缩短,我们就定义了一个,被我们称之为瞬时速度的物理量

耶鲁公开课 - 基础物理课程节选

At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.

在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度

耶鲁公开课 - 基础物理课程节选

But before you even do that, I want to define for you an important concept, which is the velocity at a given time, v .

但在这之前,我要给你们定义一个重要的概念,也就是给定时刻的瞬时速度v

耶鲁公开课 - 基础物理课程节选