9.8 快速和时间加速计算

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 从速度和时间加速计算

  Collapse Expand

  从速度和时间加速计算

  

  播放段落

  This cyclist is in constant motion as he competes in an off-road mountain bike race. Both his and his direction keep changing. is a measure that represents both speed and direction. Changes in velocity are measured by . Acceleration reflects how quickly velocity is changing. It may involve a change in speed, a change in direction, or both. 
  ::这个骑自行车的骑手不断在运动,因为他正在参加一场越野山自行车赛。他和他的方向都不断在变化。这是一个既代表速度又代表方向的尺度。速度的变化由 . 加速反映速度变化的速度。它可能涉及速度变化,方向变化,或者两者兼而有之。

  播放段落

  Calculating Average Acceleration in One Direction
  ::计算单向平均加速率

  播放段落

  Calculating acceleration is complicated if both speed and direction are changing or if you want to know acceleration at any given instant in time. However, it’s relatively easy to calculate average acceleration over a period of time when only speed is changing. Then acceleration is the change in velocity (represented by Δv) divided by the change in time (represented by Δt):
  ::如果速度和方向都在变化,或者如果您想要知道在特定时间的任何时刻加速,计算加速度是复杂的。然而,在只有速度在变化的一段时间内计算平均加速度比较容易。然后加速度是速度的变化(由 v 表示)除以时间的变化(由 t 表示):

  播放段落

  $$\begin{array}{r}\text{acceleration}=\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}\end{array}$$

  
  ::加速度t

  播放段落

  Accelerating on a Bike
  ::加速骑自行车

  播放段落

  Look at the cyclist in the Figure . With the help of gravity, he speeds up as he goes downhill on a straight part of the trail. His velocity changes from 1 meter per second at the top of the hill to 6 meters per second by the time he reaches the bottom. If it takes him 5 seconds to reach the bottom, what is his average acceleration as he races down the hill?
  ::看看图中的骑自行车者。在引力的帮助下,他随着径直的一段下坡速度加快。他的速度从山顶的每秒1公尺到到达山底的每秒6公尺。如果他需要5秒钟才能到达底部,那么他从山顶下下坡的平均加速度是多少?

  播放段落

  $$\begin{array}{rl}\text{acceleration}& =\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}\\ & =\frac{6\text{m/s}-1\text{m/s}}{5\text{s}}\\ & =\frac{5\text{m/s}}{5\text{s}}\\ & =\frac{1\text{m/s}}{1\text{s}}\\ & =1{\text{m/s}}^2\end{array}$$

  
  ::=5 m/s5 s=1 m/s1 s=1 m/s1 s=1 m/s2

  播放段落

  In words, this means that for each second the cyclist travels downhill, his velocity (in this case, his speed) increases by 1 meter per second on average. Note that the answer to this problem is expressed in m/s ² , which is the SI unit for acceleration.
  ::换句话说,这意味着骑自行车者每过一秒就下山,他的速度(在此情况下,速度)平均每秒增加1米。 请注意,这个问题的答案以m/s2表示,这是SI加速单元。

  

  播放段落

  Q: The cyclist slows down at the end of the race. His velocity changes from 6 m/s to 2 m/s during a period of 4 seconds without any change in direction. What was his average acceleration during these 4 seconds?
  ::问题 : 赛车手在赛程结束时放慢速度。 他的速度在4秒内从每秒6米/秒变为每秒2米/秒,方向没有改变。 这4秒的平均加速度是多少?

  播放段落

  A: Use the equation given above for acceleration:
  ::A: 使用上面给定的加速度方程式:

  播放段落

  $$\begin{array}{rl}\text{acceleration}& =\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}\\ & =\frac{2\text{m/s}-6\text{m/s}}{4\text{s}}\\ & =\frac{-4\text{m/s}}{4\text{s}}\\ & =\frac{-1\text{m/s}}{1\text{s}}\\ & =-1{\text{m/s}}^2\end{array}$$

  
  ::=2 m/s-6 m/s4 s @4 m/s4 s @1 m/s1 s%1 m/s2

  播放段落

  Notice that the change in velocity, or Δv, is negative because the cyclist is slowing down. This means that the acceleration is also negative, also known as a deceleration.
  ::注意速度的改变是负的, 因为骑自行车的人正在减速。 这意味着加速度也是负的, 也称为减速 。

  播放段落

  Watch the following video to learn more about how to calculate acceleration:
  ::观看以下视频以了解如何计算加速度的更多信息:

   

   

  播放段落

  Summary
  ::摘要

  播放段落
  • To calculate average acceleration when direction is not changing, divide the change in velocity by the change in time using the formula:
    $$\begin{array}{r}\text{acceleration}=\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}\end{array}$$
    
    ::要计算方向不变化时的平均加速度, 使用公式: 加速度t, 将速度变化除以时间变化 。
  播放段落
  • The SI unit for acceleration is m/s ² .
    ::加速度的SI单位为m/s2。

  播放段落

  Review
  ::回顾

  播放段落
  1. Write the equation for acceleration without a change in direction.
     ::写入加速度的方程, 不改变方向 。
  播放段落
  2. What is the SI unit for acceleration?
     ::加速度的SI单位是什么?
  播放段落
  3. During the final 5 seconds of a race, a cyclist increased her velocity from 4 m/s to 7 m/s. What was her average acceleration during those last 5 seconds?
     ::在最后5秒钟的比赛中,骑自行车者将她的速度从4米/秒提高到7米/秒。最后5秒的平均加速度是多少?