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.