It's useful to have the average acceleration, which you can find by taking similar differences of velocities.

平均加速度也是很有用的,你可以用类似方法,取速度的变化量求出来

耶鲁公开课 - 基础物理课程节选

Then, I bring the elephant and I pull the spring by the same amount and I find the acceleration of the elephant and the denominator is obviously the mass of the elephant.

然后我再找来大象,用相同的力去拉弹簧,大象就具有了加速度,很明显,分母就是大象的质量

耶鲁公开课 - 基础物理课程节选

Notice I'm using the same acceleration for both.

注意,我用的是同一个加速度

耶鲁公开课 - 基础物理课程节选

If your plan is to accelerate a 3 kg mass with an acceleration of 2 meters per second, you better have a rope that can furnish that force and it can take the tension of 6 Newtons.

如果你想用 2 米每秒平方的加速度,去拉一个 3 千克的物体,那么你就需要一根能提供拉力的绳子,并且它能够承受 6 牛的张力

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I know this is the right answer, because if I now find the acceleration, I find it's mg divided by m and I get -g as the answer for all bodies.

我知道这个等式是正确的,因为现在如果我要求物体的加速度,用 mg 除以 m,我就得到 -g,这个结果对所有物体都成立

耶鲁公开课 - 基础物理课程节选

take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.

对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r

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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