Course: 2.4 平均加速率 | The Way To Learn

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平均加速平均速度
To escape from Earth's orbit, space shuttles such as the Atlantis shown here must accelerate to 28,968 kilometers per hour, called the shuttle's escape .
::为了逃离地球的轨道,像这里展示的亚特兰蒂斯号航天飞机这样的航天飞机必须加速到每小时28 968公里,称为航天飞机的逃跑。

Average Acceleration
::平均加速平均速度

An object whose velocity is changing is said to be accelerating. Average acceleration , $\begin{aligned} \bar{a} \end{aligned}$ is defined as the rate of change of velocity, or the change in velocity per unit time. The units of are over time squared. A symbol with a bar over it is read as average – so a-bar is average acceleration.
::速度正在变化的物体据说正在加速。平均加速度,一个被定义为速度变化速度或单位时间速度变化的速度。单位在时间平方。一个带有横条的符号被以平均值读取,所以一个巴就是平均加速度。

Examples
::实例

Example 1
::例1

A car accelerates along a straight road from rest to +60.0 km/h in 5.00 s. What is the magnitude of its average acceleration?
::一辆汽车在从休息到5.00秒时每小时+60.0公里的直路上加速。平均加速度有多大?

The acceleration in this problem is read as kilometers per hour per second. In general, it is undesirable to have two different units for the same quantity in a unit expression. In this case, it is undesirable to have both hours and seconds. To eliminate this problem, we convert the hour units to seconds. Converting the original 60.0 km/h to m/s, gives 16.6 m/s.
::这一问题的加速度以每小时每秒每公里计算。一般而言, 单位表达式中不同数量有两个不同的单位是不可取的。在这种情况下, 两小时和秒都不可取。要解决这个问题, 我们将小时单位转换为秒。将原来的 60.0 公里/ 小时转换为 m/ 秒, 给出16.6 m/ 秒。

$\begin{aligned} \frac{60.0 k m}{h} \times \frac{1000 m}{1 k m} \times \frac{1 h}{3600 s} = 16.666 m / s \end{aligned}$
::60.0公里h×1000千米1公里x1x1小时3600秒=16.666米/秒

Dividing this by the time it took to achieve gives us the acceleration:
::实现这个目标需要时间, 加速了我们的速度:

$\begin{aligned} \frac{16.666 m / s}{5.00 s} = 3.33 m / s^{2} \end{aligned}$
::16.666米/秒5.00秒=3.33米/秒2

The acceleration is 3.33 m/s ² .
::加速度为3.33米/秒2。

Example 2
::例2

An automobile is moving along a straight highway in the positive direction and the driver steps on the brakes. If the initial velocity is +15.0 m/s and 5.0 s is required to slow down to +5.0 m/s, what was the car’s acceleration?
::汽车正沿着一条直高速公路向正方向行驶,司机踩刹车。如果最初的速度是+15.0米/秒和5.0秒,要减慢到+5.0米/秒,汽车加速度是多少?

$\begin{aligned} \bar{a} = \frac{Δ v}{Δ t} = \frac{- 10.0 m / s}{5.0 s} = - 2.0 m / s^{2} \end{aligned}$
::=====================================================================================================================================+=======================================================================================================================================================================================================================================================================================================================================================================================

Note that an acceleration is merely a change in velocity. This change can be either positive or negative. A negative change, such as that in the example problem above, is sometimes called negative acceleration or deceleration.
::请注意加速只是速度的变化。这种变化可以是正的,也可以是负的。负面的变化,如上面的例子问题,有时被称为负加速或减速。

Negative and Positive Acceleration
::负加速和正加速

Acceleration is a vector quantity, meaning it has both size (magnitude) and direction. The direction of acceleration depends on whether the object is speeding up or slowing down, relative to its direction of motion. In one-dimensional motion, acceleration can be either positive or negative. For example:
::加速是一个矢量, 意思是它具有大小( 磁度) 和方向。加速的方向取决于对象是加速还是放慢, 相对于其运动方向。在一维运动中, 加速可以是正的, 也可以是负的。例如 :

If an object is speeding up, the acceleration is in the same direction as its motion.
::如果一个物体正在加速,加速度与其运动的方向相同。

If an object is slowing down, the acceleration is in the opposite direction to its motion.
::如果一个物体放慢速度,加速度与其运动的方向相反。

::如果一个物体放慢速度,加速度与其运动的方向相反。

Example: Skateboarder's Motion
::示例: 滑板板人的动议

Let’s assume moving to the right is positive, and moving to the left is negative.
::让我们假设向右移动是积极的,向左移动是消极的。

A skateboarder is moving to the right. As they approach the end of the sidewalk, they slow down and eventually stop. In this case, the skateboarder's velocity is decreasing, but since they are still moving to the right (positive direction), their acceleration is negative because it opposes their motion.
::滑板机正在向右移动。当滑板机靠近人行道的尽头时,它们会放慢速度并最终停止。在这种情况下,滑板机的速度正在下降,但由于它们仍在向右移动(正向),加速速度是负的,因为它反对它们的运动。

After stopping, the skateboarder turns around and skates to the left, speeding up. Now, their velocity is increasing in the negative direction. Since both the are in the same (negative) direction, the acceleration is negative.
::停止后,滑板机转过身往左滑冰,加速了速度。现在,滑板机的速度正在向负方向上升。由于两者的方向都相同(负),加速度是负的。

Velocity-time and acceleration-time graphs can help visualize an object’s motion and calculate its average acceleration. Use the following PLIX Interactive to predict what these graphs will look like for Roger's bike ride to school.
::快速时间和加速时间图形可以帮助想象一个物体的运动并计算其平均加速度。使用以下的PLIX互动来预测罗杰骑自行车上学时这些图形会是什么样子。

Further Reading
::继续阅读

and Acceleration
::加速和加速

Summary
::摘要

Average acceleration is the rate of change of velocity, or the change in velocity per unit time.
::平均加速度是速度变化的速率,或每单位时间速度的变化。

Review
::回顾

The velocity of a car increases from +2.0 m/s to +16.0 m/s in a time period of 3.5 s. What was the average acceleration?
::在3.5秒的时间内,车速从+2.0米/秒增加到+16.0米/秒。平均加速度是多少?

If an automobile slows from +26 m/s to +18 m/s in a period of 4.0 s, what was the average acceleration?
::如果汽车在4.0秒的时间内从+26米/秒减慢到+18米/秒,平均加速度是多少?

If a runner increases his velocity from 0 m/s to +20 m/s in 2.0 s, what was his average acceleration?
::如果一个跑者将速度从0.m/s提高到2.0s的+20m/s,平均加速度是多少?

If a runner decreases his velocity from +20 m/s to +10 m/s in 2.0 s, what was his average acceleration?
::如果一个跑者将速度从+20米/秒降至2.0秒的+10米/秒,他的平均加速度是多少?

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