Part 1/5:

Understanding Derivatives through Motion Examples

The application of derivatives in calculus is foundational for understanding motion and change. This article explores the principles of differentiation by applying them to a particle's movement, discussing velocity calculations, rest points, and total distance traveled.

The Basics of Motion and Derivatives

In calculus, the motion of a particle is often described using a distance function, denoted as ( s(t) ), where ( s ) represents distance in meters and ( t ) represents time in seconds. The concept of velocity arises from the derivative of this distance function, understood as the rate of change of distance over time. Mathematically, this is expressed as:

[

v(t) = \frac{ds}{dt}

]