Kinematics Collision Question: Find Minimum Separation and Sketch

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SUMMARY

The discussion centers on a kinematics problem involving a passenger train traveling at 84 m/s and a freight train moving at 60 m/s, with the freight train's caboose 480 meters ahead. The passenger train applies brakes, decelerating at 4 m/s². The analysis concludes that the passenger train does not collide with the freight train, and the minimum separation occurs at a specific time, which can be calculated using the equation Xf - Xi = Vit + 1/2at². Sketches of position vs. time, velocity vs. time, and acceleration vs. time for both trains are also required.

PREREQUISITES
  • Understanding of kinematic equations, specifically Xf - Xi = Vit + 1/2at²
  • Knowledge of constant acceleration and deceleration concepts
  • Familiarity with graphing techniques for position, velocity, and acceleration
  • Basic understanding of relative motion in physics
NEXT STEPS
  • Calculate the time at which the minimum separation occurs using kinematic equations
  • Learn how to sketch position vs. time, velocity vs. time, and acceleration vs. time graphs
  • Explore the implications of constant deceleration in collision scenarios
  • Study more complex collision problems involving multiple objects and varying speeds
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding kinematics and collision analysis in real-world scenarios.

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Kinematics Collison question

Homework Statement


The engineer of a passenger train traveling at 84 m/s sights a freight train whose caboose is 480 meter ahead on the same track. The freight train is traveling in the same direction as the passenger train with a constant velocity of 60 m/s. The engineering of the passenger train immediately applies the brakes, causing a constant deceleration of 4 m/s2 while the freight train continues with constant speed.

a) Does the passenger train collide with freight train
b) If not, what was the minimum separation of the trains and when did this occur?
c)Draw a sketch of x vs t, v vs t and a vs t of both trains.

Homework Equations


Xf-Xi = Vit + 1/2at2
b2-4ac>0 --> no collision

The Attempt at a Solution


http://oi56.tinypic.com/os6dec.jpg
 
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