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

assuming, red train moves in positive x direction.

velocity of red train,Vr=72 i km/h=20m/s i

velocity of green train,Vg=-144 i km/h=-40 i m/s

relative velocity of red train to green=Vrg=72-(-144) km/h

=216 km/h=60i m/s

both the train are decelaerating ,there fore the direction of acceleration will be opposite to that of their velocity.

acceleration of red train,Ar=-1 i m/s^2

acceleration of green train,Ag=1i m/s^2

relative acceleration of red train to green=-2 m/s^2

by kinematic equation distance needed to travel so that both stop:-

v^2-u^2=2as

=>0-60^2=-2*2*s

=>s=900 m

but given seperation =710 m

=>they will collide

=>s=0

time taken for collision,t

=>710=60t-(0.5)*2*t^2

=>t=16.22 s

Vr=20-t i

=3.78 m/s

Vg=-40+t i

=-23.78 m/s

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