A car is stopped at an entrance ramp to a freeway; its driver is preparing to merge. At a certain moment while stopped, this driver observes a platoon of vehicles a distance x0 upstream and initiates the merge maneuver. The platoon approaches the entrance ramp at a constant speed v. The stopped car can accelerate from speed 0 to v at uniform acceleration rate a. Find the latest time at which the stopped car can safely start the merge maneuver; i.e., derive an expression for the “latest safe start time” in terms of the variables x0, v and a. Assume this latest time enables the platoon to maintain its constant speed and "just touch" the merging car's trajectory. Ignore the physical dimensions of the car.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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A car is stopped at an entrance ramp to a freeway; its driver is preparing to merge. At a certain moment while stopped, this driver observes a platoon of vehicles a distance x0 upstream and initiates the merge maneuver. The platoon approaches the entrance ramp at a constant speed v. The stopped car can accelerate from speed 0 to v at uniform acceleration rate a. Find the latest time at which the stopped car can safely start the merge maneuver; i.e., derive an expression for the “latest safe start time” in terms of the variables x0, v and a. Assume this latest time enables the platoon to maintain its constant speed and "just touch" the merging car's trajectory. Ignore the physical dimensions of the car.
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