Problem 12-31: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Question:
The velocity of a particle traveling along a straight line is v equals v-naught minus k-s, where k is a positive constant. If s equals zero when t equals zero, determine the position s as a function of time and the acceleration a as a function of time.

Kinematics via Separable ODEs: Position and Acceleration from a Velocity Law

This lesson applies first-order separable ordinary differential equations to a classical kinematics problem in which a particle's velocity depends linearly on its position. Students derive explicit expressions for position and acceleration as functions of time by separating variables, integrating, and applying an initial condition.

In this lesson, you will learn to:
• Set up and classify a first-order separable ODE from a given velocity–position relationship
• Separate variables, integrate both sides, and determine the constant of integration from an