Problem 12-19: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Rectilinear Motion with Constant Acceleration: Three-Phase Train Problem

This lesson analyzes a train journey broken into three phases — uniform acceleration from rest, constant-velocity cruising, and uniform deceleration to a stop. Students apply standard kinematic equations to find the distance covered in each phase and sum them to find the total distance between two stations.

Question:
A train starts from rest at station A and accelerates at 0.5 meters per second squared for 60 seconds. Afterwards it travels with a constant velocity for 15 minutes. It then decelerates at 1 meter per second squared until it is brought to rest at station B. Determine the distance between the stations.

In this lesson, you will learn to:
• Identify and separate a multi-phase rectilinear motion problem into distinct constant-acceleration intervals
• Apply kinematic equations ($v = v_0 + at$ and d = v_0