Problem 12-26: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Integration of Motion Equations: Position, Distance, and Velocity

This lesson demonstrates how to find a particle's velocity and position functions by integrating a time-dependent acceleration using initial conditions. It then applies those functions to determine total distance traveled by identifying direction reversals through the zeros of velocity.

Question:
The acceleration of a particle along a straight line is defined by a equals 2t minus 9 meters per second squared, where t is in seconds. At t equals 0, s equals 1 meter and v equals 10 meters per second. When t equals 9 seconds, determine: (a) the particle's position, (b) the total distance traveled, and (c) the velocity.

In this lesson, you will learn to:
• Integrate a given acceleration function to obtain velocity, applying an initial condition to determine the constant of integration.
• Integrate the velocity function to obt