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What is this critical speed?

A certain stop light stays yellow for 5 seconds before turning red. Suppose that your maximum deceleration from braking is 2 m/sec2. If you approach this light and it turns yellow, you normally have two options: If you are close enough to the light, you can continue on through at a constant speed before it turns red, while if you are far enough from the light, you can put on the brakes and stop before reaching the light. (Disregard the option of speeding up, and assume that reaction time can be ignored.) However, if you are going faster than a certain critical speed, there are some distances from the light for which you cannot do either (i.e. you are too far to make it through, and yet too close to stop). What is this critical speed?

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The explanations are in the attached PDF file.

For possible reference by Brainmass, I also past in the TEX script from which the pdf was produced - you do not have to read it as you already have the pdf file.

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Here is the plain TEX source

centerline{bf Critical speed at yellow light}

Given:
maximal deceleration $a = 2~m/s^2$,
yellow light duration $t = 5~s$.

We are looking for a situation when we are distance $x$ fro ...

Solution Summary

A certain stop light stays yellow for 5 seconds before turning red. Suppose that your maximum deceleration from braking is 2 m/sec2. If you approach this light and it turns yellow, you normally have two options: If you are close enough to the light, you can continue on through at a constant speed before it turns red, while if you are far enough from the light, you can put on the brakes and stop before reaching the light. (Disregard the option of speeding up, and assume that reaction time can be ignored.) However, if you are going faster than a certain critical speed, there are some distances from the light for which you cannot do either (i.e. you are too far to make it through, and yet too close to stop). What is this critical speed?

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