从向量计算速度 [英] computing velocity from a vector

问题描述

我说的主题正确吗?我需要一个公式来计算给定二维矢量的物体的速度.一个对象在x方向上移动+2，在y方向上移动+3.实际上，将x速度和y速度相结合，速度实际有多快?

运动单位并不是真正相关的.它实际上是一个点，该点在表单上的网格正方形上移动.我们可以将其称为每秒像素，但我认为这并不重要.我只需要总速度的公式即可.

我认为它与毕达哥拉斯定理有关，以某种相同的方式测量距离，但我无法弄清楚.我最好的猜测是

Did I phrase the subject right? What I need is a formula to computer the velocity of an object given a two-dimensional vector. An object is going +2 in the x direction and +3 in the y direction. How fast is it actually going with the x speed and y speed combined?

The unit of motion is not really relevant. It''s actually a dot moving across a grid squares on a form. We can call it pixels per second, but I don''t think it matters. I just need the formula for total velocity.

I''m thinking it has to do with the Pythagorean theorem somehow the same way distance is measured, but I can''t figure it out. My best guess is

V = Sqr((x^2) + (y^2))

有人可以帮我确认一下吗?预先感谢.

Can someone confirm that for me? Thanks in advance.

推荐答案

好，您需要相对移动(距离)并将其除以时间:

Sqrt((x-x ₀ ) ² +(y-y ₀ ) ² )/time

根据定义，速度是距离除以时间. :-)

如果在这些轴上投影所有力，坐标，速度和加速度，则始终可以单独考虑所有动力学，例如x和y(希望它们是正交的).

—SA

Well, you need relative move (distance) and divide it by time:

Sqrt((x − x₀)² + (y − y₀)²)/time

By definition, speed is a distance divided by time. :-)

You can always consider all the dynamics separately for any orthogonal coordinates like x and y (hope they are orthogonal) if you project all forces, coordinates, speeds and accelerations on these axis.

—SA

由于没有时间分量，因此您正在寻找矢量的大小.您可以按以下方式获取它:

Since there is no time component, you are looking for the magnitude of the vector. You can get it as follows:

M = Math.Sqrt(dx * dx + dy * dy)

"dx"代表"delta x"或向量的x分量. "dy"是"delta y".您可以给定任意两个x点来计算dx:

"dx" stands for "delta x", or the x component of the vector. "dy" is "delta y". You can compute dx given any two x points:

dx = x1 - x2

dy也一样.如果您确实想要速度(而不是速度，因为速度实际上只是速度和方向)，则将"M"(幅度)除以行驶该距离所花费的时间.

Same goes for dy. If you really want a speed (not a velocity, as velocity is really just speed and direction), you divide the "M" (magnitude) by the amount of time it took to travel that distance.

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