when it's okay and when it's not okay.

什么时候可以什么时候不可以
What this means is, in a time Δt,

也就是说在Δt时间内
this quantity changes by some amount,

这个变量有一定变化
and in the same time, Δt,

在同样的一段时间Δt内
that quantity changes by some amount,

这个量也发生了一定变化
then keeping the Δt equal to some number

让Δt始终保持在某一数值
we may equate the changes of the two quantities,

我们就可以认为两边的变化量相等
provided it is understood

但前提条件是
that Δ(v^(2)) is a change in v^ over 2

Δ(v^(2))是v^(2)/2在一段时间内的
in the same time in which the particle moved a distance, Δx.

变化量在这段时间内物体移动的距离为Δx
Adding the differences,

把这些变化量加起来
we eliminate time and we get this final result.

我们消去了时间得到最后的结果