Kinematics Collision Question: Find Minimum Separation and Sketch

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The discussion centers on a kinematics problem involving a passenger train and a freight train. The passenger train, traveling at 84 m/s, applies brakes to decelerate at 4 m/s², while the freight train moves at a constant speed of 60 m/s, with a 480-meter separation. The key questions are whether a collision occurs and, if not, determining the minimum separation and the time it occurs. The equations of motion are applied to analyze the situation, and the user seeks assistance with calculations and sketches of the trains' positions and velocities over time. The thread highlights the importance of understanding relative motion and deceleration in collision 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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