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A 200-meter-long train passes a pole in 10 seconds. A second 150-meter-long train moving in the same direction crosses the first train in 25 seconds. What is the speed of the second train (in m/s)?
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Calculate individual speed S1тАЛ=200/10=20 m/s. Then, calculate relative speed SRтАЛ=(200+150)/25=350/25=14 m/s. Since they move in the same direction, SRтАЛ=S1тАЛтИТS2тАЛ, so 14=20тИТS2тАЛ, which gives S2тАЛ=6 m/s.
Length of train 1 = 200m, time to pass pole = 10s, length of train 2 = 150m, time to cross each other = 25s, direction = same.
Speed=TimeDistanceтАЛ,Relative┬аSpeed=Time┬аto┬аCrossSum┬аof┬аLengthsтАЛ
Calculate individual speed S1тАЛ=200/10=20 m/s. Then, calculate relative speed SRтАЛ=(200+150)/25=350/25=14 m/s. Since they move in the same direction, SRтАЛ=S1тАЛтИТS2тАЛ, so 14=20тИТS2тАЛ, which gives S2тАЛ=6 m/s.
Students often add the speeds (assuming opposite direction) instead of subtracting them for the same direction relative speed calculation.
Calculate speed of first train
The first train covers its own length to pass a pole. Using speed = distance / time:
S1тАЛ=10200тАЛ=20┬аm/s
Calculate relative speed
When two trains move in the same direction, the total distance covered is the sum of their lengths. The relative speed is the ratio of this distance to the time taken:
SRтАЛ=25200+150тАЛ=25350тАЛ=14┬аm/s
Determine speed of the second train
For same-direction movement, SRтАЛ=S1тАЛтИТS2тАЛ. Substituting the known values:
14=20тИТS2тАЛтЯ╣S2тАЛ=20тИТ14=6┬аm/s
A is correct because the calculated speed of the second train is 6 m/s.
This concept of relative speed is frequently applied in boat and stream problems and circular motion problems in competitive exams.