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Homework Statement:

Two trains are traveling on the same linear track but in opposite direction and toward each other. The train on the right is moving to the left with a velocity of 54 m/s and the train on the left is moving to the right with a velocity of 38 m/s. When the brakes are fully applied on the train on the right, the ensuing acceleration has a magnitude of 0.31 m/s2.
Given the trains have their breaks applied simultaneously and come to a stop at exactly the same instant,
determine the minimum distance between the trains at which they could fully apply their brakes and come to a complete halt without colliding.
determine the acceleration of the train on the left.
Relevant Equations:

x= 1/2at^2+Vot+Xo
a= delta v/t
So my work includes using the acceleration formula a=delta v/t
(VrtfVrti)/a > (054)/(0.31) > t=174 seconds
I plug in 174 seconds to find the acceleration of the left train. and got 0.22m/s^2
I then used the displacement equation
x=(1/2)at^2+Vo+So
coming out with Xrt=4703m and Xlt= 3281m
I subtracted those coming out with 1422m, which is the minimum distance between each train to safely halt without crashing.
is that right?!
(VrtfVrti)/a > (054)/(0.31) > t=174 seconds
I plug in 174 seconds to find the acceleration of the left train. and got 0.22m/s^2
I then used the displacement equation
x=(1/2)at^2+Vo+So
coming out with Xrt=4703m and Xlt= 3281m
I subtracted those coming out with 1422m, which is the minimum distance between each train to safely halt without crashing.
is that right?!