Problem 12-17: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Minimum Following Distance to Avoid Collision (Kinematics)

This lesson applies one-dimensional particle kinematics to determine the minimum safe following distance between two vehicles undergoing sequential braking. It combines constant-velocity and constant-deceleration motion phases, and uses the condition of zero relative velocity to identify the critical instant of minimum gap.

Question:
Car B is traveling a distance d ahead of car A. Both cars are traveling at 60 feet per second when the driver of car B suddenly applies the brakes, causing car B to decelerate at 12 feet per second squared. It takes the driver of car A 0.75 seconds to react, which is a normal driver reaction time. When car A's driver applies the brakes, car A decelerates at 15 feet per second squared. Determine the minimum distance d between the cars so as to avoid a collision.

In this lesson, you will learn to:
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