# 直線運動

## 位移

${\displaystyle \Delta x=x_{2}-x_{1}}$

## 速度

### 平均速度

${\displaystyle \mathbf {\overline {v}} ={\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {\mathbf {x} _{2}-\mathbf {x} _{1}}{t_{2}-t_{1}}}}$

${\displaystyle t_{1}}$是物体位移为${\displaystyle \mathbf {x} _{1}}$时的时间，
${\displaystyle t_{2}}$是物体位移为${\displaystyle \mathbf {x} _{2}}$时的时间。

### 瞬时速度

${\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\Delta \mathbf {x} \over \Delta t}}$

## 加速度

${\displaystyle \mathbf {\overline {a}} }$表示平均加速度，${\displaystyle \Delta \mathbf {v} =\mathbf {v} _{2}-\mathbf {v} _{1}}$是速度在时间变化量${\displaystyle \Delta t}$中的变化，那么，

${\displaystyle \mathbf {\overline {a}} ={\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {\mathbf {v} _{2}-\mathbf {v} _{1}}{t_{2}-t_{1}}}}$

${\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}$

## 运动学方程

${\displaystyle \mathbf {v_{f}} =\mathbf {v_{i}} +\mathbf {a} \mathbf {t} \;\!}$
${\displaystyle \mathbf {d} =\mathbf {v_{i}} \mathbf {t} +{\begin{matrix}{\frac {1}{2}}\end{matrix}}\mathbf {a} \mathbf {t} ^{2}}$
${\displaystyle {\mathbf {v_{f}} }^{2}={\mathbf {v_{i}} }^{2}+2{\mathbf {a} }\mathbf {d} }$
${\displaystyle \mathbf {d} ={\tfrac {1}{2}}\left(\mathbf {v_{f}} +\mathbf {v_{i}} \right)\mathbf {t} }$

## 参考文献

1. ^ Resnick, Robert and Halliday, David (1966), Physics, Section 3-4
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7. ^ Speed & Velocity. [2021-06-29]. （原始内容存档于2021-11-15）.
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9. ^ Average Velocity, Straight Line. [2021-06-29]. （原始内容存档于2021-11-15）.
10. ^ Acceleration. （原始内容存档于2011-08-08）.
11. What is the term used for the third derivative of position?. [2021-06-29]. （原始内容存档于2016-11-30）.
12. ^ Equations of motion (PDF). [2021-06-29]. （原始内容存档 (PDF)于2013-06-26）.
13. ^ Description of Motion in One Dimension. [2021-06-29]. （原始内容存档于2017-07-09）.
14. ^ What is derivatives of displacement?. [2021-06-29]. （原始内容存档于2014-05-31）.
15. ^ Linear Motion vs Rotational motion (PDF). [2021-06-29]. （原始内容存档 (PDF)于2021-04-17）.

## 参考书目

• Resnick, Robert and Halliday, David (1966), Physics, Chapter 3 (Vol I and II, Combined edition), Wiley International Edition, Library of Congress Catalog Card No. 66-11527
• Tipler P.A., Mosca G., "Physics for Scientists and Engineers", Chapter 2 (5th edition), W. H. Freeman and company: New York and Basing stoke, 2003.