A red train traveling at 72 km/h and a green train traveling at 144 km/h are hea

Question

A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed   toward each other along a straight, level track. When they are 710 m apart, each engineer sees the other's   train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s2. Is there a collision?   
If so, give (a) the speed of the red train, (b) the speed of the green train, and   (c) the separation between the trains when they collide (0 m).  
If not, give (a) the speed of the red train (0 m/s), (b) the speed of the green train (0 m/s), and   (c) the separation between the trains when they stop.

Explanation / Answer

Combined speed of two train = 144+72 =216 km/h= 60 m/sec
Speed of red train = 20 m/sec
Speed of green train = 40 m/sec
Deaccelration = 1m/s^2 for each train
Distance between = 710 m
distance before red train stops = U^2/2a= 20*20/2 = 200 m
distance before green train stops = U^2/2a= 40*40/2 = 800 m
so train collide
train collide after t time = 710/60 =11.833 sec
a) speed of red train = 20-11.833= 8.166 m/sec = 29.4 Km/hr
b) speed of green train = 40-11.833 = 28.166 m/sec = 101.4 Km/hr
c) distance b/w them = 0

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