Help with decelleration, acceleration and time

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To solve the problem of deceleration and acceleration between two trains, use the formula v² - u² = 2as, where u is the initial velocity, v is the final velocity, s is displacement, and a is acceleration. This equation allows for the calculation of displacement (s) and subsequently time (t). The scenario involves one train slowing down and stopping while the other continues at cruising speed, creating a time separation at the next station. Understanding the relationship between acceleration, deceleration, and time is crucial for determining the time gap between the two trains. Accurate calculations will provide the necessary time separation as they pass through the station.
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Hi, welcome to PF.

You need to use v^{2}-u^{2}=2as where u is the initial velocity, v the final, s is the displacement and a is the acceleration. From this you can find s and then find t.
 
You have everything you need.

Imagine two trains running together on parallel tracks. One slows down, stops for a while and then accelerates back to cruising speed. The other one is now a good way ahead. What you have to find is the time separation between these two trains as they pass through the next station without stopping.
 
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