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It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
  • a)
    2.0
  • b)
    10.0
  • c)
    12.0
  • d)
    22.0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
It takes 10 s and 15 s, respectively, for two trains travelling at dif...
Speed of the first train = length/time = 120/10 = 12m/s
Speed of the second train = length/time = 150/15 = 10m/s
2.0 m/s is the difference in the train speed.
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Most Upvoted Answer
It takes 10 s and 15 s, respectively, for two trains travelling at dif...
Given data:
Length of first train (l1) = 120 m
Length of second train (l2) = 150 m
Time taken by first train to pass the telegraph post (t1) = 10 s
Time taken by second train to pass the telegraph post (t2) = 15 s

Let the speed of the first train be v1 m/s and the speed of the second train be v2 m/s.

Calculations:
1. Speed of the first train (v1):
We know that distance = speed × time
Length of the first train + Distance travelled by the first train in 10 s = Distance travelled by the second train in 10 s
Therefore, l1 + v1 × 10 = v2 × 10
v1 = (v2 × 10 - l1) / 10

2. Speed of the second train (v2):
Using the same formula, we get
l2 + v2 × 15 = v1 × 15
v2 = (v1 × 15 - l2) / 15

3. Difference in speeds:
Substituting the value of v1 in the second equation, we get
v2 = (15v2 - l1v2 - l2) / 150
14v2 = l1v2 + l2
v2 = (l1 + l2) / 14
Substituting this value of v2 in the first equation, we get
v1 = (v2 × 10 - l1) / 10
v1 = ((l1 + l2) / 14) × (10 / 15) - (l1 / 10)
v1 = (3l1 - 2l2) / 420

Therefore, the magnitude of the difference in speeds of the two trains is given by
|v1 - v2| = |(3l1 - 2l2) / 420 - (l1 + l2) / 14|
|v1 - v2| = |(3l1 - 2l2 - 30l1 - 30l2) / 420|
|v1 - v2| = |(-27l1 - 32l2) / 420|
|v1 - v2| = |-9l1/140 - 8l2/105|

Substituting the given values of l1 and l2, we get
|v1 - v2| = |(-9 × 120 / 140) - (8 × 150 / 105)|
|v1 - v2| = 2.0 m/s

Therefore, the correct option is (a) 2.0.
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It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds tocompletely pass a telegraph post. The length of the first train is 120 m and that of the second train is150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.a)2.0b)10.0c)12.0d)22.0Correct answer is option 'A'. Can you explain this answer?
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