# Trains

A train is said to have crossed an object (stationary or moving) only when the last coach of the train crosses the said object completely. It implies that the total length of the train has crossed the total length of the object.
• Time taken by a train to cross a pole/a standing man

• Time taken by a train to cross platform/bridge etc. (i.e. a stationary object with some length)

• When two trains with lengths L1 and L2 and with speeds S1 and S2 respectively, then
1. When they are moving in the same direction, time taken by the faster train to cross the slower train
2. When they are moving in the opposite direction, time taken by the trains to cross each other
• â€¢ Suppose two trains or two bodies are moving in the same direction at u km/hr and v km/hr respectively such that u > v, then their relative speed = (u â€“ v) km/hr.

If their lengths be x km and y km respectively, then time taken by the faster train to cross the slower train (moving in the same direction) = hrs.
• Suppose two trains or two bodies are moving in opposite directions at u km/hr and v km/hr, then their relative speed = (u + v) km/hr.

If their lengths be x km & y km, then : time taken to cross each other =  hrs.
• If a man is running at a speed of u m/sec in the same direction in which a train of length L meters is running at a speed v m/sec, then (v â€“ u) m/sec is called the speed of the train relative to man. Then the time taken by the train to cross the man =  seconds
• If a man is running at a speed of u m/sec in a direction opposite to that in which a train of length L meters is running with a speed v m/sec, then (u + v) is called the speed of the train relative to man.

Then the time taken by the train to cross the man  seconds.