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
there's a needle and the needle says 60;

有一根指针指着60
that's your velocity at this instant.

表示你这个时刻的速度
It's very interesting

这非常有趣
because velocity seems to require two different times to define it --

因为速度似乎需要两个时间才能算出来
the initial time and the final time.

初时刻和末时刻