I NEED HELP. THE ONLY INFORMATION PROVIDED THANKS. Two trains A und B ure travel

Question

I NEED HELP. THE ONLY INFORMATION PROVIDED THANKS.

Two trains A und B ure traveling in opposite directions 50mi/lu and train B is trav their brakes. They each decelerate at 200mie. Do they are they each going when they crush? If not, how far aprt are one mile apart, both engineers apply ht 200mihr. Do they crash i other? If so, how fast If not, how fur apart are they when they come to rest? inoot directions on the same track. Train A is traveling veling ROmi/hr, When they are one mile apart e crash into each ohy fast inmo each

Explanation / Answer

speed of train A = 50 mi/hr

speed of train B = 80 mi/hr

acceleration = a = -200 mi/hr2

final speed of each = Vf =0

consider the motion of train A

Using the equation

Vf2 = Vi2 + 2 a d

0 = 502 + 2 (-200) d

d = 6.25 mi

hence stopping distance of A is greater than 1 mi, so the trains crash into each other

Let the train crash after time 't'.

train A covers distance 'X'

train B covers distance '1-X'

For train A :

X = 50 t - 100 t2                 Eq-1

For train B :

1- X = 80 t - 100 t2              Eq-2

Adding equation 1 and 2

1 = 130 t - 200 t2

t = 0.008 hr

speed of train A after time 't'

Vf = Vi + at

Vf = 50 - 200 (0.008)

Vf = 48.4 mi/hr

speed of train B after time 't'

Vf = Vi + at

Vf = 80 - 200 (0.008)

Vf = 78.4 mi/hr

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