Two trains R and S start from rest simultaneously from stations A and B facing each other with
accelerations 0.5 m/s2 and 2/3 m/s2 reaching their maximum speeds of 90 kmph and 72 kmph
respectively. If they cross each other midway between the stations, find the distance between the
stations and the time taken by each other.
Answers
Answer:
65 sec
2 km
Step-by-step explanation:
Two trains R and S start from rest simultaneously from stations A and B facing each other with accelerations 0.5 m/s2 and 2/3 m/s2 reaching their maximum speeds of 90 kmph and 72 kmph respectively. If they cross each other midway between the stations, find the distance between the stations and the time taken by each other.
Distance S = ut + (1/2)at²
u = initial speed 0 m/s at rest
v = u + at
v = final speed m/s
a = acceleration m/s²
let say after t sec both train meet each other
Final speed of Train R = 90 km/Hr = 90 * 1000/3600 = 25 m/s
25 = 0 + (0.5)t
t = 50 sec
S = 0 + (1/2)(0.5)50² = 625 m
after that train will move with final speed
Distance covered in t sec= 25*(t-50) + 625 = 25t - 625 m
Final speed of Train S = 72 km/Hr = 72 * 1000/3600 = 20 m/s
20 = 0 + (2/3)t
t = 30 sec
S = 0 + (1/2)(2/3)30² = 300 m
after that train will move with final speed
Distance covered in t sec = 20(t-30) + 300 = 20t - 300 m
as both trains meet midway so both distances are equak
25t - 625 = 20t - 300
=> 5t = 325
=> t = 65 sec
After 65 secs both train will meet ( for cross over train length required)
Distance covered in 65 Sec by train R = 25*65 - 625 = 1000m
Distance covered in 65 Sec by train S = 20*65 - 300 = 1000m
Total distance between A & B station = 1000m + 1000m = 2000 m
= 2km