If you're taking two derivatives you can add a constant and something linear in t.

如果你要二次求导,你可以添加一个一次项和常数项

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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

耶鲁公开课 - 基础物理课程节选

You can add something else to the answer without invalidating it, and that is anything with one power of t in it, because if you take one derivative it'll survive, but if you take two derivatives, it'll get wiped out.

你可以往答案后面加上其它东西,而且不影响结果,也就是任何t的一次项,因为你求一次导数之后它还在,但如果你求两次导数,这一项就不存在了

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