Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.

只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数

耶鲁公开课 - 基础物理课程节选

It knows that this particle happened to have a height of 15, at the time of 0, and a velocity of 10, and it is falling under gravity with an acceleration of -10.

这个质点恰好处在高度为15的地方,零时刻,初速为10,并在重力作用下以-10的加速度下坠

耶鲁公开课 - 基础物理课程节选

At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.

在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度

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Even at=0, and it has an initial velocity, so even without any acceleration, it will be moving from y0 to y0+vt.

即使at=0,它仍然有初速度,因此即使加速度为0,它也会从y0运动到y0+vt

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So, we know in this example the initial height should be 15 meters and the initial velocity should be 10, and for acceleration, I'm going to use -g and to keep life simple, I'm going to call it -10.

我们知道在这个例子中,初始高度为15米,初始速度为10,然后是加速度,我们用"-g"表示重力加速度,为了计算方便,加速度的值取为-10

耶鲁公开课 - 基础物理课程节选