A little later, which is t+Δt.

一小段时间后也就是t+Δt时刻
So Δt is going to stand always for a small finite integral of time;

Δt总是用来代表一个极短的时间间隔
infinitesimal interval of time not yet 0.

不为零的无穷小时间间隔
So, during that time, the particle has gone from here to there,

在这段时间内粒子会从这里运动到这里
that is x+Δx,

即x+Δx的地方
and the average velocity in that interval is Δx/Δt.

这段时间的平均速度等于Δx/Δt
Graphically, this guy is Δx

在图中这一段是Δx
and this guy is Δt, and Δx/Δt is a ratio.

这一段是Δt Δx/Δt是一个比值
So in calculus, what you want to do

从微积分的角度看你想要做的
is to get the notion of the velocity right now.

是马上得到速度的概念
We all have an intuitive notion of velocity right now.

我们现在都有一个对速度的直观概念
When you're driving in your car,

当你在开车时