Problem 12-29: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Rectilinear Motion with Variable Acceleration

This lesson covers how to analyze the motion of two particles moving along a straight line under variable acceleration by integrating acceleration to find velocity and position. Students learn to determine the separation between particles at a given instant and to calculate total distance traveled by identifying direction reversals.

Question:
Two particles A and B start from rest at the origin s equals 0 and move along a straight line such that the acceleration of A equals 6t minus 3 feet per second squared, and the acceleration of B equals 12t squared minus 8 feet per second squared, where t is in seconds. Determine the distance between them when t equals 4 seconds, and the total distance each has traveled in t equals 4 seconds.

In this lesson, you will learn to:
• Integrate variable acceleration functions to obtain velocity and position