Instantaneous acceleration

Gist: The derivative of velocity with respect to time — equivalently, the second derivative of position.

$a_t={\lim }_{\Delta t\to 0}\frac{V_{t+\Delta t}-V_t}{\Delta t}a=\frac{dv}{dt}=\frac{d^{2}x}{d{t}^2}$

Why it matters: The same limiting move as instantaneous velocity, applied one level up. Position, velocity and acceleration form a single chain of derivatives, which is why constant acceleration makes position a quadratic in $t$.

Detail: Lecture 2, p.4

Related: Average acceleration, Instantaneous velocity, Kinematic equations, Physics