Problem 12-23: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Kinematics with Velocity-Dependent Acceleration

This lesson solves a particle motion problem where acceleration is given as a function of velocity, $a = -2v$. By treating the kinematic relationships as separable first-order ODEs, students derive position, velocity, and acceleration as explicit functions of time using integration and initial conditions.

Question:
A particle moves along a straight line with acceleration defined as a equals negative 2v meters per second squared, where v is in meters per second. Given that v equals 20 meters per second when s equals 0 meters and t equals 0 seconds, determine the position, velocity, and acceleration as functions of time.

In this lesson, you will learn to:
• Set up and solve a first-order separable ODE for velocity when acceleration is a function of velocity
• Apply initial conditions to determine constants of integration for both velocity