Math, asked by mahalakshmi524, 1 year ago

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

Answered by amitnrw
3

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

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