but I want to derive the formula and put it up,

但是我想重新推导一遍
then we'll see how to use it.

再来看如何进行运用
Second formula tries to relate the final velocity of some time, t,

第二个式子能把某段时间t的末速度
to the initial velocity and the distance traveled

和初速度经过的路程联系在一起
with no reference to time.

并且不引入时间
So the trick is to eliminate time from this equation.

所以这里的技巧就是消去方程中的时间
So let's see how we can eliminate time.

我们来看看如何消去它
You know that if you took a derivative of this,

如果你对这个式子求一次导
you will find v of t is v0+at.

你将会得到v(t)=v0+at
What that means is,

这个方程的意义是
if you know the velocity of the given time

如果你知道某个给定时刻的速度
and you know the initial velocity,

并且知道初速度