Problem 12-9: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Kinematics of a Particle: Velocity, Position, and Total Distance via Integration

This lesson demonstrates how to find a particle's velocity and position functions by integrating a time-dependent acceleration along a straight line. It also covers how to determine total distance traveled by checking for direction reversals using the velocity function.

Question:
The acceleration of a particle as it moves along a straight line is given by a equals 2t minus 1, in meters per second squared, where t is in seconds. If s equals 1 meter and v equals 2 meters per second when t equals 0, determine the particle's velocity and position when t equals 6 seconds. Also determine the total distance the particle travels during this time period.

In this lesson, you will learn to:
• Integrate a given acceleration function to obtain velocity as a function of time, applying initial conditions.
• Integrate th