Agniveer Army CEE Trains

Train problems involve calculating time taken by trains to cross objects like poles, platforms, bridges, or other trains. The key is understanding that trains have length, unlike point objects

When a train crosses a stationary object like a pole, it travels a distance equal to its own length. When crossing a platform or bridge, it travels its own length plus the length of the platform/bridge. For two trains, use relative speed concept.

Distance covered = Length of train = 120m

Time taken = 8 seconds

Speed = Distance/Time = 120/8 = 15 m/s

Convert to km/hr = 15 × 18/5 = 54 km/hr Answer: 54 km/hr Worked Example 2: Two trains of lengths 100m and 150m are running in opposite directions at speeds 40 km/hr and 50 km/hr respectively. In how much time will they cross each other?

Convert speeds to m/s: 40 km/hr = 40 × 5/18 = 100/9 m/s, 50 km/hr = 50 × 5/18 = 125/9 m/s

Relative speed = 100/9 + 125/9 = 225/9 = 25 m/s (opposite direction, so add)

Total distance = 100 + 150 = 250m

Time = Distance/Speed = 250/25 = 10 seconds Answer: 10 seconds Advanced Shortcut - Platform Formula: Time to cross platform = (Train length + Platform length)/Speed. This direct formula saves calculation steps in exams. Most Common Trap: Students forget to add platform/bridge length when train crosses them. They only consider train length, leading to wrong answers. Always read whether the train crosses a pole (only train length) or platform/bridge (train length + platform/bridge length). Another frequent mistake is wrong unit conversion. Practice the 5/18 conversion thoroughly. Many students confuse when to multiply or divide. Speed-Distance-Time Shortcut: If train crosses pole in time T1 and platform in time T2, then platform length = speed × (T2 - T1). This eliminates the need to calculate train length first.