What is the final distance between two decelerating trains on a straight track?

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Two trains, initially 1.2 km apart and traveling towards each other at 100 km/h and 128 km/h, begin to decelerate at 0.9 m/s² upon seeing each other. The equations for displacement under constant deceleration are applied to determine the distance each train travels before stopping. The first step involves calculating the time it takes for each train to stop using the formula v(t) = v₀ - at. Once the stopping times are found, these values are plugged into the displacement equations to find how far apart the trains will be when they stop. The discussion emphasizes the importance of calculating each train's stopping distance to determine their final separation.
ellusion
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hi I am new to this and i have a problem that I am stumped on.

Two trains, one traveling at 100km/h and the other at 128km/h, are headed towards one aanother along a straight level track. When the trains are 1.2km apart, each engineer sees the other train and applies the brakes. Both trains have equal, constant decelerations of 0.9 m/s^2. What is the distance they will be apart?
 
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I suggest you first write down the equations for displacement in the case of constant acceleration (i.e. deceleration), and present us some attempts.
 
well this is what i have,

d=vt - 1/2at^2 and i believe i should find the time it takes

a= 0.9m/s^2 = 3.24km/h^2

Train 1
1.2 = 100t - 1/2(3.24)t^2
0= -1.2 + 100t - 1.62t^2

then i use the quadratic eqn to solve for t. am i on the right track?
 
Calculate the time it takes for every train to stop separately out of the equation v(t) = v_{0} - at = 0. Then, plug the times t into the equations for displacement for each train separately and calculate the distance each train travels until it stops. It should be fairly easy to find how far they are apart from each other now.
 
ahh okay thanks for the help
 

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