# 動能

${\displaystyle E_{k}={\frac {1}{2}}mv^{2}}$，當中

${\displaystyle m}$ 係物體嘅質量${\displaystyle v}$ 係物體嘅速度

## 背景

### 力同作功

${\displaystyle W=\mathbf {F} \cdot \Delta \mathbf {r} \,}$，或者寫做
${\displaystyle W=m\mathbf {a} \,\cdot \Delta \mathbf {r} \,}$

${\displaystyle W=\int _{C}\mathbf {F} (\mathbf {r} )\cdot \mathrm {d} \mathbf {r} \,}$

### 推導動能

{\displaystyle {\begin{aligned}v^{2}&=v_{0}^{2}+2a\left(r-r_{0}\right)\\\end{aligned}}}

${\displaystyle \mathbf {a} ={v^{2}-v_{0}^{2} \over 2\left(r-r_{0}\right)}}$，即係
${\displaystyle \mathbf {a} ={v^{2}-v_{0}^{2} \over 2\Delta \mathbf {r} }}$，跟住代呢條式落去功嗰條式（${\displaystyle W=m\mathbf {a} \,\cdot \Delta \mathbf {r} \,}$）嗰度嘅話就會出到
${\displaystyle W=m\Delta \mathbf {r} \cdot \,{v^{2}-v_{0}^{2} \over 2\Delta \mathbf {r} }}$，跟住一路執：
${\displaystyle W=m\cdot \,{v^{2}-v_{0}^{2} \over 2}}$
${\displaystyle W={{1 \over 2}mv^{2}}-{{1 \over 2}mv_{0}^{2}}}$

## 註釋

1. Δr = rfinalrinitialrfinal 係件物體最後個位置，而 rinitial 係佢初頭個位置。

## 攷

1. Movement means energy 互聯網檔案館歸檔，歸檔日期2018年1月6號，..
2. Naito, K., Takagi, H., & Maruyama, T. (2011). Mechanical work, efficiency and energy redistribution mechanisms in baseball pitching. Sports Technology, 4(1-2), 48-64.
3. Conservative Force. HyperPhysics.