Two trains 100 m and 80 m long, respectively are running in opposite directions. Trains A running with constant velocity 10 m/s and train B, start from rest and running with uniform acceleration 5 m/s2. If the initial separation between two trains is 80 m Then after what time they meet each other (In second)
Answers
Answer:
hence,A1:a2:a3
=1:3:3
Given : Two trains 100 m and 80 m long, respectively are running in opposite directions.
Train A running with constant velocity 10 m/s and
train B, start from rest and running with uniform acceleration 5 m/s².
the initial separation between two trains is 80 m
To Find : after what time they meet each other
Solution:
To meet each other they need to cover 80m distance
To cross each other they need to cover 80 + 100 + 80 = 260 m distance
Let sat after t secs they meet each other need to cover 80m distance
S = vt for constant velocity
S = ut + (1/2)at² for constant acceleration
Distance covered by train A = 10t m
Distance Covered by train B = 0 + (1/2)5t² m
10t + (1/2)5t² = 80
=> 20t + 5t² = 160
=> 4t + t² = 32
=> t² + 4t - 32 = 0
=> (t + 8)(t - 4) = 0
t = 4 as time can not be negative
Hence trains meet after 4 secs
Additional Info :
Train cross each other need to cover 260m distance
10t + (1/2)5t² = 260
=> 4t + t² = 104
=> t² + 4t - 104 = 0
t ≈ 8.392 sec
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