# 基础力学/直线运动

## 分析质点直线运动的运动学方程

${\displaystyle \mathbf {r} =\mathbf {r} (t)=x(t)\mathbf {i} }$

${\displaystyle x=x(t)}$

${\displaystyle v={\frac {\mathrm {d} x}{\mathrm {d} t}},\quad a={\frac {\mathrm {d} v}{\mathrm {d} t}}={\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}.}$

${\displaystyle x=x(t)=x_{0}+v_{x}t}$

${\displaystyle v=x'(t)=v_{x}}$

${\displaystyle x=x(t)=x_{0}+v_{0}t+{\frac {1}{2}}a_{x}t^{2}}$

{\displaystyle {\begin{aligned}v&=x'(t)=v_{0}+a_{x}t\\a&=x''(t)=a_{x}\end{aligned}}}

${\displaystyle v^{2}-v_{0}^{2}=2a_{x}x}$

## 求解质点直线运动的运动学方程

${\displaystyle v=x'(t)={\frac {\mathrm {d} x}{\mathrm {d} t}}}$

${\displaystyle x=\int v(t)\mathrm {d} t=x(t)+C}$

${\displaystyle C=x_{0}-x(t_{0})}$

${\displaystyle x-x_{0}=x(t)-x(t_{0})}$

${\displaystyle x(t)-x(t_{0})=\int _{t_{0}}^{t}v(t)\mathrm {d} t}$

${\displaystyle x=x_{0}+\int _{t_{0}}^{t}v(t)\mathrm {d} t}$

${\displaystyle \Delta x=x-x_{0}=\int _{t_{0}}^{t}v(t)\mathrm {d} t}$

${\displaystyle a=v'(t)={\frac {\mathrm {d} v}{\mathrm {dt} }}}$

${\displaystyle v=\int a(t)\mathrm {d} t=v(t)+C}$
${\displaystyle v=v_{0}+\int _{t_{0}}^{t}a(t)\mathrm {d} t}$
${\displaystyle \Delta v=v-v_{0}=\int _{t_{0}}^{t}a(t)\mathrm {d} t}$