He found that some droplets had a certain velocity, and then others had a velocity plus some step.

他发现了一些液滴存在某个速度，还有其他的液滴有速度和位移。

麻省理工公开课 - 固态化学导论课程节选

If I gave you the location of a particle as a function of time, you can find the velocity by taking derivatives.

如果我给出物体的位移是时间的函数,你可以通过求导来得到速度

耶鲁公开课 - 基础物理课程节选

And he couldn't get values of velocity in between certain steps.

他得不出两个点之间,位移的速度。

麻省理工公开课 - 固态化学导论课程节选

They tell you the initial location and initial velocity of the object.

它们表示的是物体的初始位移,和初始速度

耶鲁公开课 - 基础物理课程节选

Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.

只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数

耶鲁公开课 - 基础物理课程节选

For example, if you started here and you did all this and you came back here, the average velocity would be zero, because you start and end at the same value of x, you get something; 0 divided by time will still be 0.

例如,如果你从这里开始运动,经过这个过程又回到这里,平均速度就是0,因为初态和末态的位移相同,你得到了什么呢,0除以时间还是0

耶鲁公开课 - 基础物理课程节选

Then, in every situation where the body has an acceleration a, the location has to have this form, where this number is where it was initially, this was the initial velocity of the object.

在任何研究对象具有加速度a的情况下,它的位移就一定具有这种形式,这个系数代表了它的初位移,这个代表了它的初速度

耶鲁公开课 - 基础物理课程节选