Train Collision Calculation: Red Train vs Green Train on 950 km Track"

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SUMMARY

The discussion focuses on a collision scenario between a red train traveling at 72 km/h (20 m/s) and a green train at 144 km/h (40 m/s) on a 950 km track. Both trains apply brakes with a deceleration of 1.0 m/s² upon seeing each other. Calculations reveal that the trains will collide, as their stopping distances do not exceed the initial separation of 950 km. The final speeds at impact can be determined using kinematic equations.

PREREQUISITES
  • Understanding of kinematic equations, specifically the equation x = x0 + v0T + (1/2)(x - x0)
  • Knowledge of unit conversions, particularly converting kilometers to meters and hours to seconds
  • Familiarity with concepts of acceleration and deceleration in physics
  • Basic problem-solving skills in physics to analyze motion scenarios
NEXT STEPS
  • Calculate the stopping distance for both trains using the formula d = v² / (2a)
  • Explore the impact of different deceleration rates on collision outcomes
  • Investigate real-world applications of train braking systems and safety measures
  • Learn about relative motion and how it applies to multiple moving objects
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion, as well as educators looking for practical examples of train dynamics and collision analysis.

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Homework Statement


A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward one another along a straight, level track. When they are 950 km apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 1.0 m/s^2. Is there a collision? If so, what is the speed of each train at impact? If not, what is the separation between the trains when they stop?


Homework Equations


x=x0 + v0T + (1/2)(x - x0)


The Attempt at a Solution


I tried using the above equation, but I could not get a reasonable answer. I changed everything to meters and seconds. Here are the changes for those units:

95 km = 950,000 m
221 km/h = 61.39 m/s
 
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Just split it into two equations, and find the distance it takes to stop each one.
 

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