Problems On Trains
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- $$a\ km/hr = a×\frac{5}{18}m/s$$
- $$a\ m/s = a×\frac{18}{5}km/hr$$
- Speed of the Train = Total distance covered by the train / Time taken
- Note: Time taken by a train of length L metres to pass a pole or a standing man or a post is equal to the time taken by the train to cover L metres.
- If a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.
- If two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = (u – v) m/s.
- If two trains or two bodies are moving in the opposite direction at u m/s and v m/s, then their relative speed is = (u + v) m/s.
- If length of two trains a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken to cross each other = (a+b)/(u+v) sec.
- If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then faster train to cross the slower train = (a+b)/(u-v) sec.
- If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A’s speed) : (B’s speed) = (√ b∶ √ a )
1 A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
2 A train 110 metres long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
3 The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is
4 How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length?
5 Without stoppage, the speed of a train is 54 km/h and with stoppage, it is 45 km/h. For how many minutes, does the train stop per hour?
6 A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
7 A 110 m long train is running at a speed of 60 km/h. How many seconds, does it take to cross an another train of length 170 m, which is standing on parallel track?
8 A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?
