A classic physics topic that relates to derivatives is velocity and acceleration in kinematics.

1. Velocity as the derivative of position: Velocity represents the rate of change of position with respect to time. If is the position of an object as a function of time , then the velocity is the first derivative of the position function:

2. Acceleration as the derivative of velocity: Acceleration is the rate of change of velocity with respect to time. If is the velocity, then the acceleration is the first derivative of velocity, or equivalently, the second derivative of position:

In this way, derivatives are used to describe how physical quantities like position, velocity, and acceleration are related to each other through rates of change.

https://effectuall.github.io/Simulations/Mechanics_Angular_Momentum.html

$$ v(t) = \frac{dx(t)}{dt} $$

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