Acceleration

Core Sentence / 核心句

Acceleration is the instantaneous rate of change of velocity and the second derivative of position.

中文理解：加速度描述速度随时间怎样变化，也是位置对时间的二阶导数。

Formula / 公式或规则

$$a(t)=\frac{dv}{dt}=\frac{d^{2}s}{d{t}^2}$$

Speed Test / 速率判断

• $v$ and $a$ same sign -> speeding up
• $v$ and $a$ opposite signs -> slowing down

Watch Out / 易错点

negative acceleration 不必然是 slowing down；它只表示 velocity 正向负方向变化。

Search and Source Mentions / 搜索与出现位置

Mentioned In / 出现位置

• 微积分BC第4次正课 · Motion Derivative Chain
  • acceleration is velocity’s derivative and position’s second derivative
• Chapter 10 · Motion Derivative Chain
• Chapter 10 · Speed Test

Connected Notes / 连接

• 微积分BC第4次正课-反函数高阶导数与运动应用
• One-Dimensional Motion
• 10 - Higher Order Derivatives
• Second Derivative
• Higher-Order Derivatives
• Instantaneous Rate of Change
• Newton’s Second Law