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# 牛頓第二定律??

V=VO + at

S=vot+2分之1at平方

v平方=vo平方+2as

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1.英文阿......好難喔

這是轉貼的:

Newton's second law of motion explains how an object will change velocity if it is pushed or pulled upon.

Firstly, this law states that if you do place a force on an object, it will accelerate, i.e., change its velocity, and it will change its velocity in the direction of the force.

Secondly, this acceleration is directly proportional to the force. For example, if you are pushing on an object, causing it to accelerate, and then you push, say, three times harder, the acceleration will be three times greater.

Thirdly, this acceleration is inversely proportional to the mass of the object. For example, if you are pushing equally on two objects, and one of the objects has five times more mass than the other, it will accelerate at one fifth the acceleration of the other.

2.三角函數

In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers. All of these approaches will be presented below.

In modern usage, there are six basic trigonometric functions, which are tabulated below along with equations relating them to one another. (Especially in the case of the last four, these relations are often taken as the definitions of those functions, but one can equally define them geometrically or by other means and derive the relations.)

(來源:維基百科Wikipedia，網址:http://en.wikipedia.org/wiki/Trigonometric_functio...

先作一些名稱上的約定(請在白紙上畫一個直角三角形):

假設一個直角⊿ABC，其中∠C為直角。∠A與∠B是互餘的兩個銳角。

AB為三角形的斜邊，∠B所對應的邊AC稱為「對邊」，與∠B相鄰但不是斜邊的另外一個BC稱為「鄰邊」。

∠B的函數值如下:

sin(sine)-----正弦=對邊/斜邊=AC/AB

cos(cosine)-----餘弦=鄰邊/斜邊=BC/AB

tan(tangent)-----正切=對邊/鄰邊=AC/BC

cot(cotangent)-----餘切=鄰邊/對邊=BC/AC

sec(secant)-----正割=斜邊/鄰邊=AB/BC

csc(cosecant)-----餘割=斜邊/對邊=AB/AC

那如果換成∠A:

sinA=BC/AB

cosA=AC/AB

tanA=BC/AC

cotA=AC/BC

secA=AB/AC

cscA=AB/BC

3.這三個是等加速的運動公式

其中V代表「末速」，Vo代表「初速」，a代表「加速度」，t代表「時間」，

S(Δx)是位移。

<證明>

1.第一個公式V=Vo+at應該蠻直觀的，由加速度a的定義a=ΔV/t就知道了，其中ΔV是速度的變化量，也就是末速-初速(V-Vo)。

a=(V-Vo)/t經過移項整理就得到V=Vo+at。

2.畫圖來證明好了:

http://tw.pg.photos.yahoo.com/ph/lubrige2/detail?....

3.根據第一式與第二式得到的結果:

第一式整理成t=(V-Vo)/a，然後代進第二公式

ΔX=Vo[(V-Vo)/a]+1/2(a)[(V-Vo)/a]²

嗯...麻煩妳自己整理一下囉，整理出來就是V²=Vo²+2(a)(ΔX)#

舉例的話，假設某物一開始以8m/s的速度前進，以2m/s²的加速度加速到10m/s，那位移就代入第三公式(10²=8²+2*2*ΔX)，整理之後就可以得到位移，時間的話就代等加速第一公式(10=8+2*t)，整理之後就可以得到時間。

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補:牛頓第二運動定律

Newton's second law: fundamental law of dynamics

The acceleration of an object equals the total force acting on it, divided by its (constant) mass.

m is the mass of the object in question,

F is the total force acting on the object

a is the object's acceleration, i.e., the rate of change of its velocity with respect to time

For example, if a bowstring exerts a constant force of 100 newtons on an arrow having a mass of 0.10 kg, then the arrow's acceleration will be 1000 m/s2 until it leaves the bow (after which the arrow will stop speeding up).

When the forces on the object all act along the same line, they can be added as positive and negative numbers, depending on their direction. When they do not all act along the same line, the total must be found by vector addition.

The quantity m, or mass, is a characteristic of the object. The greater the total force acting on an object, the greater the change in its acceleration will be. This equation, therefore, indirectly defines the concept of mass.

In the equation, F = ma, a is directly measurable but F is not. The second law only has meaning if we are able to assert, in advance, the value of F. Rules for calculating force include Newton's law of universal gravitation.

這是Wikipedia的資料，解釋得應該更為完備，因為我等級不夠，有些圖像的說明文字沒辦法轉貼，所以附上網址，請您自行參考:

http://en.wikipedia.org/wiki/Newton's_laws_of_moti...

(我覺得一開始貼的那一篇寫得沒有維基百科這篇好，還是以這一篇為主好了)

大致就是這樣，參考看看吧^^

Source(s): 已個別標註

Newton's second law :

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. As learned in the "The Rocket Simulation" Lab, the acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force of propulsion acting upon the rocket-chair increased, the acceleration of the rocket-chair increased. As the mass of the rocket-chair increased, the acceleration of the rocket-chair decreased.

trigonometric function ：

A function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, and cosecant. Also called circular function.

V=VO + at

S=vot+2分之1at平方

v平方=vo平方+2as

以上這些公式是由牛頓第二運動定律演變而來的3大公式, 這3個公式可以計算出所有運動狀態下的未知數......也就是可以解所有的力學的題目啦 ~~~~

舉例來說: 1物體從靜止開始自由落體落下, 3秒後該物體的速度 V=V0+at = 0+9.81*3=29.43m/s......其他以此類推 ~~~~