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Take the difference of the two velocities and divide by the difference of the two times, and you've got the acceleration.
求出速度的差值,除以时间的差值,这样就能得到加速度
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Why should the amount by which you're attracted to the Earth be also a measure of how much you hate acceleration?
为什么物体受地球引力的大小,恰好能衡量物体加速的难易程度呢
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If every time I get the same acceleration, I'm convinced this is a reliable spring that is somehow producing the same force under the same condition.
如果每次都能得到相同的加速度,这个弹簧的可靠性就能令人信服,即它在相同的条件下能够产生相等的力
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The fact that when you step on your gas you accelerate, everybody knows.
所有人都知道踩油门就能加速
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That's connected to mass times acceleration.
然后就能和质量乘以加速度联系上了
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You cannot say to me, "Take a force, due to a spring, and see what force it applies and divide by the acceleration and get the mass, " because we haven't defined force, either.
你不能说,"给弹簧施加一个力,看看它能提供多大的力,然后除以加速度,得到质量",因为我们还没给力下一个定义
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Newton tells you forces cause acceleration.
牛顿告诉我们,力能产生加速度
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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
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That's how by either balancing the unknown force with a known force or by simply measuring the acceleration as I fall towards this podium and multiplying by mass, you can find the force that exerts on me.
我们既可以让未知力与已知力平衡,也可以只测量我冲向讲台时加速度的大小,再与我的质量相乘,都能求出作用在我身上的力的大小
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So, the question we are going to ask is the following, "If I tell you that a particle has a constant acceleration a, can you tell me what the position x is?"
接下来要问的问题就是,如果我说某质点加速度恒为a,你能告诉我它的位移x是多少吗
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The most important result from last time was that if you took this r, and you took two derivatives of this to find the acceleration, d^2 r over dt^2, try to do this in your head.
上节课最重要的结论,就是如果你把 r 写成这样,对 r 求两次导就能得到加速度,d^2 r / dt^2,心算一下
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