Problem 12-24: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Particle Velocity from a Position-Dependent Acceleration

This lesson demonstrates how to find a particle's velocity as a function of position when acceleration is given as a function of position. The method uses the chain-rule kinematic identity a = v dv/ds to convert the problem into a separable ordinary differential equation, which is then integrated with an initial condition.

Question:
The acceleration of a particle traveling along a straight line is a equals one-fourth times the square root of s, in meters per second squared, where s is in meters. If v equals zero and s equals one meter when t equals zero, determine the particle's velocity at s equals two meters.

In this lesson, you will learn to:
• Apply the kinematic identity a = v dv/ds to relate acceleration, velocity, and position without using time.
• Separate variables and integrate both sides of a differential equation usi