2.2 平均速率

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  平均速率

  

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  Test Pilot Neil Armstrong (later to become a famous astronaut) is seen here next to the X-15 ship after a research flight. The servo-actuated ball nose, seen at Armstrong's right hand, provided accurate measurement of air at hypersonic speeds. The X-15 was flown over a period of nearly 10 years, and set the world's unofficial speed record of 4,250 mph.
  ::实验飞行员尼尔·阿姆斯特朗(Neil Armstrong)(后来成为著名宇航员)在研究飞行后,在X-15号飞船旁边出现。 在阿姆斯特朗右手所见的脉冲球鼻子提供了超声波速度的准确空气测量。 X-15号飞机飞行了近10年时间,将世界非官方速度记录设定为4,250米。

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  Average
  ::平均平均数

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  In ordinary language, the words speed and velocity both refer to how fast an object is moving, and are often used interchangeably. In physics , however, they are fundamentally different. Speed  is the magnitude of an object's motion, with no regard for the direction. Velocity is the speed and direction at which an object is moving. It is a vector , and thus must have a magnitude and a direction.
  ::在普通语言中,单词速度和速度都指一个物体移动的速度,而且经常被互换使用。但在物理学中,速度是完全不同的。速度是指一个物体运动的大小,不考虑方向。速度是指一个物体移动的速度和方向。它是一个矢量,因此必须有一个大小和方向。

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  Average speed is calculated by dividing the total travelled by the time interval. For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph). Average velocity, however, involves total displacement , instead of distance. It is calculated by dividing the total displacement by the time interval. In this example, the driver's displacement is zero, which makes the average velocity zero mph. 
  ::平均速度的计算方法是将总行驶时间间隔除以总行驶时间间隔。例如,驾驶20英里向北,然后向南20英里(最终在同一地点),平均速度为40英里除以40分钟,或每分钟1英里(60英里)。但是,平均速度涉及全部移位,而不是距离。计算方法是将总移位除以时间间隔。例如,驾驶员的移位为零,因此平均速度为零。

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  Neither average speed nor average velocity implies a constant rate of motion. That is to say, an object might travel at 10 m/s for 10 s and then travel at 20 m/s for 5 s and then travel at 100 m/s for 5 s. This motion would cover a distance of 700 m in 20 s and the average speed would be 35 m/s. We would report the average speed during this 20 s interval to be 35 m/s and yet at no time during the interval was the speed necessarily 35 m/s.
  ::平均速度和平均速度均不意味着运动的恒定速度。也就是说,一个物体可以以10米/秒的速度飞行10秒,然后以20米/秒的速度飞行5秒,然后以100米/秒/秒的速度飞行5秒。这个运动将覆盖20秒中700米的距离,平均速度为35米/秒。我们将报告这20秒中的平均速度为35米/秒,而在间隔中,速度不一定为35米/秒。

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  Constant velocity is very different from average velocity. If an object traveled at 35 m/s for 20 s, it would travel the same distance in the same time as the previous example but in the second case, the object's velocity would always be 35 m/s.
  ::恒定速度与平均速度大不相同。如果一个物体在35米/秒以内飞行20秒,则其飞行距离与上一个示例相同,但在第二个示例中,该物体的速度始终为35米/秒。

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  Example
  ::示例示例示例示例

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  The position of a runner as a function of time is plotted as moving along the $\begin{array}{r}x\end{array}$ -axis of a coordinate system.  During a 3.00 s time interval, the runner’s position changes from $\begin{array}{r}{x}_1=50.0\text{m}\end{array}$ to  $\begin{array}{r}{x}_2=30.5\text{m}\end{array}$ . What was the runner’s average velocity?
  ::运行者的时间函数位置被绘制成坐标系统 x 轴的移动。 在 3. 00 时间间隔期间, 运行者的位置从 x1 = 50.0 m 到 x2 = 30.5 m 。 运行者的平均速度是多少?

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  $\begin{array}{r}\text{Displacement}=30.5\text{m}-50.0\text{m}=-19.5\text{m}\end{array}$ (the object was traveling back toward zero)
  ::移位=30.5 m- 50.0 m19.5 m( 对象返回零)

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  $\begin{array}{r}\mathrm{\Delta }t=3.00\text{s}\end{array}$
  ::T=3.00秒

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  $\begin{array}{r}{v}_{\text{ave}}=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{-19.5\text{m}}{3.00\text{s}}=-6.50\text{m/s}\end{array}$
  ::5米3.00秒6.50米/秒

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  Observe the differences between constant velocity and average velocity in the simulation below where two silly robots, Irwin and Ruthie, are racing to the elevator:
  ::观察以下模拟中恒定速度和平均速度的差别, 在模拟中, 两个愚蠢的机器人,Irwin和Ruthie, 正在比赛升降机:

   

   

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  Another important aspect of velocity is that it is always measured relative to something. We usually measure how fast a person walks or how fast a car drives relative to the ground. In Astronomy, we often measure the motion of the Earth relative to the Sun. A reference frame is a fixed point and we measure directions relative to it.
  ::速度的另一个重要方面是它总是相对于某物进行测量。我们通常测量一个人行走的速度或汽车行驶速度相对于地面的速度。在天文学中,我们常常测量地球相对于太阳的动向。一个参照框架是一个固定点,我们测量相对于它的方向。

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  Use the following simulation to explore what happens when two bikers approach each other at various velocities and be sure to click on different observers each time to observe their motion from different reference frames:
  ::使用以下模拟来探究当两个骑自行车的人在不同速度上相互接近时会发生什么情况,并且确保每次点击不同的观察者,观察他们从不同参照框架运动的情况:

   

   

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  Further Reading
  ::继续阅读

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  Summary
  ::摘要

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  • Average speed is distance divided by time.
    ::平均速度是距离除以时间间隔。
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  • Average velocity is displacement divided by time.
    ::平均速度是迁移时间除以。

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  Review
  ::回顾

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  1. On a one day vacation, Jane traveled 340 miles in 8.0 hours.  What was her average speed?
     ::在一天的假期里,简在8小时的8小时里旅行了340英里 她的平均速度是多少?
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  2. An object on a number line moved from x = 12 m to x = 124 m and moved back to x = 98 m. The time interval for all the motion was 10 s.  What was the average velocity of the object?
     ::数字线上的一个物体从x = 12米移到x = 124米,然后回移到x = 98米。 所有运动的时间间隔为 10 秒。 该物体的平均速度是多少?
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  3. An object on a number line moved from x = 15 cm to x = 165 cm and then moved back to x = 25 cm, all in a time of 100 seconds.
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     1. What was the average velocity of the object?
        ::物体的平均速度是多少?
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     2. What was the average speed of the object?
        ::物体的平均速度是多少?
     
     ::数字线上的一个对象从 x = 15 cm 到 x = 165 cm,然后在 100 秒内全部回移到 x = 25 cm。该对象的平均速度是多少? 该对象的平均速度是多少?

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  Explore More
  ::探索更多

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  Use  this resource to answer the question that follows.
  ::使用此资源回答以下问题 。

   

   

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  1. What is the main difference between average speed and average velocity?
     ::平均速度和平均速度之间的主要差别是什么?