How Do You Calculate the Minimum Deceleration to Prevent a Train Collision?

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To prevent a collision between a passenger train and a freight train, the passenger train must decelerate from 32.0 m/s to a maximum speed of 27.0 m/s. The minimum required deceleration was calculated to be approximately -0.347 m/s². The passenger train will travel a certain distance before reaching this speed, and the time taken to stop can be determined using kinematic equations. The initial separation of 425 meters must be considered to ensure no collision occurs. Understanding the relationship between acceleration, time, and velocity is crucial for solving this problem effectively.
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Kinematics Train Crash Question

Homework Statement



A passenger train is behind a freight train, both on the same set of tracks and moving in the same direction. The freight train is moving at a constant speed of 27. 0 m/s and maintains that speed. The passenger train is originally moving at 32. 0 m/s when the engineer of the passenger train spots the freight train and applies the brakes. At the time the brakes are ap- plied, the separation between the trains is 425. 0 meters, and the application of the brakes causes the passenger train to have a constant acceleration in the direction opposite to the train’s velocity.

A) If there is to be no collision, what must the minimum value of the magnitude of the ac- celeration of the passenger train?

B) Assuming this minimum value, how far will the passenger train travel before it stops, and what will be the minimum separation between the trains? How much time will it take the passenger train to stop?

C) Draw a single position-time diagram showing both trains from the initial spotting of the freight train to the stopping of the passenger train. This should be a carefully drawn graph with appropriate labels and scales.​

Homework Equations



d=27t+425
d=32t+(1/2)at^2

The Attempt at a Solution



I've been focusing mostly on Part A so far. I used the equations I posted above to try to substitute a and t for each other. I got t=14.4 and a=-.347. When I plug "a" back into the equation I noticed that the two functions are no where near touching each other. Not sure where to really go from here. I'm pretty sure I can solve the rest of the problem if I understood how to find the correct acceleration value.

Thanks ahead of time for the responses.
 
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To avoid collision, the passenger train does not need to stop when it reaches the freight train. It is enough if it slows down to its speed, 27.0 m/s. The relation among acceleration, time and change of velocity is the third equation you need for the solution.

ehild
 

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