But then having found one answer,

一旦你算出了一个答案
you can add to it anything

你就可以往式子里加入任何
that gets killed by the act of taking derivatives.

在求完导后消失的项
If you're taking only one derivative you can add a constant.

如果只进行一次求导你可以添加一个常数项
If you're taking two derivatives you can

如果你要二次求导
add a constant and something linear in t.

你可以添加一个一次项和常数项
If you knew only the third derivative of the function,

如果方程里有三阶导数
you can have something

你就可以引入一个二次项
quadratic in t without changing the outcome.

但是结果却不会变
So, this is the most general position

这是一个加速度为a的匀加速质点
for a particle of constant acceleration, a.

位移的最一般的表达式
You must remember that

务必记住