来自《耶鲁大学开放课程：基础物理第2集第2集》

for every value of time,

在每一个时间点
you can put the numbers in

你可以把数值代入
and you can find the velocity by just taking derivatives.

并通过求导得到速度
The derivative of this guy will be 2t times i plus what?

这个式子的导数为 i ? 2t 加上什么呢
Rule for taking derivatives,

按求导法则来做
if you want to do this mindless application of calculus,

如果你想解决这个微积分的简单应用
you can do it.

你可以很容易做到
i and j are constant,

i 和 j 是常矢量
ignore them when you take derivatives.

求导的时候可以忽略它们
x and y are dependent on time.

x 和 y 坐标都是时间的函数
Just take the derivatives and that's the velocity vector.

直接计算对时间的导数就是速度矢量
You can take a derivative of the derivative

你可以对导数再求一次导