Minimum Deceleration for Railroad Crossing Accident Avoidance

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Homework Help Overview

The problem involves a scenario where an engineer must determine the minimum deceleration required to stop a locomotive before reaching a car stuck on the tracks. The context includes initial speed, distance to the crossing, and the engineer's reaction time.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using kinematic equations to calculate the distance traveled during the reaction time and the subsequent deceleration needed to stop the train. There are varying interpretations of the time and distance calculations, with some questioning the assumptions made about constant speed and the correct formulas to use.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some have provided partial calculations and suggested alternative equations, while others are clarifying the assumptions and parameters involved in the scenario.

Contextual Notes

Participants are working under the constraints of the problem as posed, including the specified initial conditions and the requirement to avoid an accident. There is uncertainty regarding the correct application of kinematic equations and the interpretation of time variables.

runner1738
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An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 210 m from the crossing and its speed is 10 m/s. If the engineer's reaction time is .22 s, what should be the magnitude of the minmum deceleration to avoid an accident? Answer in units of m/s^2
 
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runner1738 said:
An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 210 m from the crossing and its speed is 10 m/s. If the engineer's reaction time is .22 s, what should be the magnitude of the minmum deceleration to avoid an accident? Answer in units of m/s^2
First, use the formula d=vt to find the distance he travels before applying the brakes. Subtract that distance from 210 m. Then, use the formula:
[tex]d=V_it + \frac{1}{2}at^2[/tex]
to find the acceleration, which would be a negative number.
 
wait but shouldn't i solve for time 210=10(t) then t is 21 then 21-.22=20.78 then 210=10(20.78)+1/2(a)(20.78)^2 so a = .0101897345
 
No, since his speed is not 10 m/s throughout. First, find the DISTANCE he travels in 0.22s (d=(10 m/s)(0.22s)).
 
210-2.2=d=207.8=10(22)+1/2(a)(22)^2 ? ? or is 21.78 for time?
 
runner1738 said:
210-2.2=d=207.8=10(22)+1/2(a)(22)^2 ? ? or is 21.78 for time?
You got the first part (the 207.8m) right. As for the rest, you canot use 22s and the time, since you don't know the time it will take hime to stop. (Sorry, I gave you the wrong formula).
Ok, here's what you know:
initial velocity=10 m/s
final velocity = 0 m/s (since he has to stop)
d = 207.8 m
a=?

Can you find a formula that fits?
 
runner1738 said:
210-2.2=d=207.8=10(22)+1/2(a)(22)^2 ? ? or is 21.78 for time?

Where are you getting t=22?

I wouldn't use the above equation.

There's a different distance equation you can use and solve for "a" immediately... hint: it doesn't have a t in it.
 
how is time 17.21 seconds i have 207.8=10t-1/2(.2406)t^2
 

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