Two trains, traveling toward one another on a straight track, are 100 m apart wh

Question

Two trains, traveling toward one another on a straight track, are 100 m apart when the engineers on both trains become aware of the impending collision and hit their brakes. The eastbound train, initially moving at 85 km/h, decelerates at 4 m/s2. The westbound train, initially moving at 130 km/h, slows down at 4 m/s2. Will the trains stop before colliding? If not, what initial separation would have been needed to avert a disaster? (Give the minimum distance necessary. If not applicable, enter NAN.)

Explanation / Answer

Here,

for the eastbound train ,

initial speed, u = 85 km/hr

u = 23.61 m/s

a = -4 m/s^2

for the distance d1 of first train

-2 * 4 * d1 = 0 - 23.61^2

d1 = 69.7 m

NOw, for the westbound train

initial speed, u = 130 km/hr

u = 36.1 m/s

a = -4 m/s^2

for the distance d2 of second train

-2 * 4 * d2 = 0 - 36.1^2

d2 = 163 m

hence , more distance than 100 m is needed for the trains to stop

- NO the trains will not stop before colliding.

initial seperation needed = d1 + d2

initial seperation needed = 69.7 + 163

initial seperation needed = 232.7 m

the initial seperation needed for non collision is 232.7 m  

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