Explore Amtrak's 20th-Century Limited: A Cow's Tale

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Homework Help Overview

The problem involves a train, Amtrak's 20th-Century Limited, which is traveling from Chicago to New York and encounters a cow on the tracks. The train's speed, braking time, and the need to determine the distance from the cow when brakes were applied are central to the discussion. The subject area includes kinematics and motion under constant acceleration.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the train's acceleration and direction, with some confirming their understanding of these aspects. Questions arise regarding the appropriate equations to use for calculating the distance from the cow when the brakes were applied, with references to various kinematic equations.

Discussion Status

Some participants have successfully identified the acceleration and its direction, while others are exploring different equations to find the distance. There is an ongoing exchange of ideas, with no clear consensus yet on the best approach to solve for the distance.

Contextual Notes

Participants note the historical context of the train service, mentioning that the 20th Century Limited ceased operations in 1967, which may influence the framing of the problem. There is also a mention of potential confusion regarding the application of kinematic equations.

imac
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Homework Statement


Amtrak's 20th-Century Limited is in route from Chicago to New York at 112 km/h, when the engineer spots a cow on the track. The train brakes to a halt in 2.3 min, stopping in front of the cow.

a) What is the magnitude of the train's (constant) acceleration?
_______m/s^2 <-----(0.22m/s^2) Correct

b) What is the direction of the acceleration?
- eastward
- westward <-----Correct
- southward
- northward

c) How far was the train from the cow when the engineer first applied the brakes?
______km

The Attempt at a Solution


I have a) and b) correct but I can't figure out c).

Thanks.
 
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reverse it. imagine the train is accelerating at 0.22 m/s/s
 


imac said:

Homework Statement


Amtrak's 20th-Century Limited is in route from Chicago to New York at 112 km/h, when the engineer spots a cow on the track. The train brakes to a halt in 2.3 min, stopping in front of the cow.

a) What is the magnitude of the train's (constant) acceleration?
_______m/s^2 <-----(0.22m/s^2) Correct

b) What is the direction of the acceleration?
- eastward
- westward <-----Correct
- southward
- northward

c) How far was the train from the cow when the engineer first applied the brakes?
______km

The Attempt at a Solution


I have a) and b) correct but I can't figure out c).

Thanks.

First what equation do you know that relates distance acceleration and time?

(Btw, I think the 20th Century Limited stopped running in 1967. Today it's the Lake Shore Limited that runs the route.)
 


LowlyPion said:
First what equation do you know that relates distance acceleration and time?

(Btw, I think the 20th Century Limited stopped running in 1967. Today it's the Lake Shore Limited that runs the route.)

I know this equation but I get the wrong answer: d=(vf^2-vi^2)/2a
 


imac said:
I know this equation but I get the wrong answer: d=(vf^2-vi^2)/2a

I would have simply used the x = 1/2 a t2 relationship.

x = 1/2 * .22544 * (138 sec)2

The other equation works as well

x = (31.111)2/(2*(.22544))
 

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