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And know intuitively that if they move together, they will behave like an object of mass 5 and the acceleration will again be 2.
凭直觉认为既然它们一起运动,那么它们就相当于一个质量为 5 千克的物体,然后我们可以算出加速度为 2
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A limited class of problems is one in which the acceleration is just a constant.
在这类有限的问题里,加速度均为常数
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Then you guys know, you just told me, acceleration is -9.8, We call it "minus" because it's accelerating down and up was taken to be the positive direction.
然后你们都知道,你告诉我,加速度是-9.8,我们取负号是因为加速度方向朝下,而正方向为竖直向上
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So you cannot use the formula once it hits the ground because once it hits the ground, the fundamental premise that a was a constant of -9.8 or -10 is wrong.
当物体落地以后,该公式就不适用了,因为当物体落地后,公式的基本前提——,加速度为常数-9.8或-10——就不成立了
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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
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If you knew this was one kilogram, then the acceleration of the elephant, which will be some tiny number, maybe 100th of what this guy did; the mass of the elephant is then 100 kilograms.
如果已知这个物体的质量为 1 千克,那大象的加速度,会是一个比较小的数,可能是物体加速度的 1 / 100,大象的质量就是 100 千克
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I want to consider a particle which has definite acceleration a, a constant one, but a is now a vector.
我想考虑一个加速度为 a 的质点,加速度恒定,但 a 是一个矢量
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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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You're only given the particle has acceleration a, and you are asked to find out what is x?
你只知道质点的加速度为a,你需要求出x是多少
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That means the acceleration is pointing towards the center of the circle and it has a magnitude a.
也就是说加速度,始终指向圆心,其模长为 a
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You can easily check by taking two derivatives that this particle does have the acceleration a.
你可以很容易地通过求两次导来验证,这个质点的加速度确实为 a
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So, this is the most general position for a particle of constant acceleration, a.
这是一个加速度为a的匀加速质点,位移的最一般的表达式
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Whenever you see a particle moving in a circle, even if it's at a constant speed, it has an acceleration, v square over r directed towards the center.
只要看到质点做圆周运动,即使是匀速圆周运动,也存在一个加速度,大小为 v^2 / r,方向指向圆心
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So, this certainly describes a particle whose acceleration is a.
它确实描述了一个加速度为a的质点的运动
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If it's going in a circle, you will say from now on, that it, indeed, has an acceleration, even though no one's stepping on the accelerator, of amount v^2 over R.
如果它在一个圆周上运动,你会说从现在起它其实有加速度,即使没有人去踩油门,加速度大小为 v^2 / R
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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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Right. The most famous example is that when things fall near the surface of the Earth, they all have the same acceleration, and the acceleration that's common is called g, and that's 9.8 m/s^.
最有名的例子就是,当物体地球表面附近下落时,它们都拥有相同的加速度,这个普遍的加速度叫做g,大小为9.8m/s^
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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
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