solve Two trains are approaching each other on the same railroad track. Train A

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Two trains are approaching each other on the same railroad track. Train A initially moving with a speed of 40.0 m/s and Train B is initially moving with a speed of 30.0 m/s. When the train conductors realize that they are approaching each other, they both start to brake their trains. Train A brakes with an acceleration magnitude of 8.00 m/s^2 and Train B brakes with an acceleration magnitude of 7.50 m/s^2 (a) If the trains begin to brake when they are 200 m apart, will they collide or will they stop before they collide? (b.) If the trains do not collide, how far apart will they be when they stop? lf the trains do collide, how fast will they be moving when they collide?

Explanation / Answer

Initial speed of car A is u = 40 m/s

Accleration of car A is a = -8 m/s 2

Final speed of car A is v = 0

From the relation v 2 - u 2 = 2aS

Distance travel before stop S = (v 2 - u 2 ) / 2a

= (0 2 - 40 2 ) /2(-8)

= 100 m

Initial speed of car B is U = 30 m/s

Accleration of car B is a ' = -7/5 m/s 2

Final speed of car B is V = 0

From the relation V 2 - U 2 = 2a 'S '

Distance travel before stop S ' = (V 2 - U 2 ) / 2a '

= (0 2 - 30 2 ) /2(-7.5)

= 60 m

Total distance travel by both carA and B before stop = S +S ' = 100 + 60 = 160 m

i.e., A and B are not collide.

Separation of cars A and B after stop = 200 m - 160 m = 40 m

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