Investigate the factors that affect the STOP and GO Zones at intersections with traffic lights
Investigate the factors that result in an Overlap Zone or a Dilemma Zone at intersections with traffic lights
Use a computer simulation to mathematically model the situations that can occur at an intersection with traffic lights
What do you see/What do you think 11/3
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What do you see?I see the red car stopping short at a red light and stops in the middle on an intersection. The dog is flying out of the car. The green car is speeding up and going through the red light. What do you think?The yellow light should have been longer because the red car couldn't stop in time. It had to stop in the middle of the intersection. The green car is doing an illegal act because it is going through the red light.
Stop Zone/Go ZoneNovember 14th
Go_Zone.jpg
Investigation:Friday, November 4th
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3a.)Will automobile B be able to make it through the intersection?Yes, because automobile B cannot just come to a sudden stop with cars behind him3b.)Is automobile B in the go zone?yes B is, because B has no time to stop, or does not have enough distance left until the middle of the intersection.3c.)Would any automobile closer to the intersection that automobile A be in the Go Zone?Yes, because the closer you are with a yellow light, the more reason you have to continue through.3d.)Is automobile C in the go zone?No, and if C decided to continue, then they would
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4a.)Is autopmobile E in the stop zone?Yes, because it is too far away from the yellow light to stop.4b.)Is automobile F in the stop zone? Explain your answer.No automobile F is in the Go zone, because they have enough room to stop. PG 95-96 PART B
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A-YesB-YesC-NoD-No
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E-YesF-YesH-NoG-No
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J-YesL-NoM-YesK-Yes
Go Zone/Stop Zone Notes:November 17th
GoZone
StopZone
Vi (speed limit) ty (yellow light time) w (width of intersection) a (negative acceleration)
Vi (speed limit) ty (yellow light time) w (width of intersection) a (negative acceleration) tr (reaction time)
Go Zone Prediction/Actual Results:
Screen_shot_2011-11-07_at_5.27.18_PM.png
Stop Zone Prediction/Actual Results:
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Part B: Yellow Light Dilemma pg. 95November 18th1a. Automobiles A and D should stop, and B and C should go.2a. Automobiles E and F should stop, H has the choice, and G should go.3a. Automobiles J and L should stop, M has the choice, and K should go.4a. Intersection I has a distint STOP and GO Zone. Intersection II has an overlap that could be part of either the STOP or GO Zone. Intersection III has a Dilemma Zone.4b. Your choices are to either go or stop. It would be safe to do either because the zones are unclear.4c. Your choices are to either go or stop. Neither is safe because that area is neither a STOP Zone nor a GO Zone.4d. Intersection II has an Overlap Zone and Intersection III has a Dilemma Zonw. Go Zone/Stop Zone EquationsNovember 18thGo Zone:
v = d/t v = d/ty v = (w + GZ) / ty GZ = (v)(ty) - w (The furthest distance at which you can go safely...where the Go Zone ends)
Stop Zone: SZ = TSD SZ = dr + dB SZ = Vitr - (Vi)^2 / 2a The closest position to the intersection in which you can brake safely...where the Stop Zone begins)
Checking Up Questions November 18th
1. In this section, the spreadsheet is referred to as a model. What makes it a model? A model is a mathematical equation to better understand a problem. 2. In your own words, describe what is meant by the GO Zone. The GO Zone includes all positions where the automobile can safely proceed through the intersection when the light turns yellow. 3. In your own words, describe what is meant by the STOP Zone. The STOP Zone includes all positions where the car can safely stop before reaching the intersection. 4. Describe what is meant by the Overlap Zone. In the Overlap Zone, when the light turns yellow, the driver of the vehicle has the choice of either stopping or going through the intersection safely before the light turns red. 5. Describe what is meant by the Dilemma Zone. The Dilemma Zone is a space between the STOP and GO Zones. In this region, a driver traveling the speed limit cannot safely stop before the intersection or pass through the intersction completely before the light turns red. Only occurs in a poorly designed intersection.
Active Physics Plus: November 19th
1.Given a car approaching an intersection of width 25 m and yellow light time 3 seconds on a road of speed limit 45 mph (20 m/s) with a maximum deceleration of -5 m/s2 and a driver with reaction time .7 seconds. Diagram the intersection, calculate the Stop Zone and Go Zone, and decide if the intersection is safe or dangerous and explain why. w = 25 m ty = 3 s Vi = 20 m/s a = -5 m/s tr = .7 s -- GZ = (Vi)(ty) - w GZ = (20)(3) - 25 GZ = 35 m -- SZ = (Vi)(tr) - (Vi^2/(2a) SZ = (20)(.7) - (20^2)/(2)(-5) SZ = 54 m
APP_chap_1_sect_6_#1.jpg
2. Design 3 separate realistic and safe intersections. A realistic intersection has an overlap zone that is 10-30 m long. Re-compute the Stop Zones and Go Zones using the stop zone and go zone formulas then diagram the 3 safe intersections and photo them along with the calculations into your wiki. Check your intersections using the excel sheet to make sure its safe before you calculate the stop zone and go zone using the formulas.
2a.jpg
2a.png
2b.jpg
2b.png
2c.png
3.Design 1 safe intersections for a cognizant driver of reaction time .5 sec and maximum deceleration of -6 m/s2. Choose the other 3 variables(speed limit, yellow light time and width of intersection) to make a safe and realistic intersection. A realistic intersection has an overlap zone that is 10-30 m long. You can use the excel sheet and do not have to use the manual formulas to calculate Stop Zone and Go Zone. Diagram them and list the 1 input variables under the photo of the diagram in your wiki.
3_APP_chap_1_sect_6.jpg
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4.Design 1 safe intersections for a fatigued driver with reaction time 2 seconds and maximum deceleration of -4 m/s2. Choose the other 3 variables(speed limit, yellow light time and width of intersection) to make a safe and realistic intersection. A realistic intersection has an overlap zone that is 10-30 m long. You can use the excel sheet and do not have to use the manual formulas to calculate Stop Zone and Go Zone. Diagram them and list the 5 input variables under the photo of the diagram in your wiki.
4_APP_chap_1_sect_6.jpg
Screen_shot_2011-11-11_at_8.21.48_AM.png
HW 10/9 1. The Go Zone would shrink because it would take longer to cross the intersection if it were wider. 2. The driver could change the velocity to increase the Go Zone. 3. The driver with bad brakes has to stop first, has a longer TSD, and has a Stop Zone pushed back farther away from the intersection. 4. The faster driver has a longer TSD and has a Stop Zone pushed back farther from the intersection. 5. The drunk driver has a longer TSD and has a Stop Zone pushed back farther from the intersection. 6. Speed affects the Stop Zone more because the variable "v" is used twice in the SZ equation. The Stop Zone is extended if you are going faster.
Go Zone/Stop Zone of a Real Intersection November 13th
Intersection 5:Kinderkamack and Prospect Ave. in Woodcliff Lake
Screen_shot_2011-11-13_at_12.58.55_PM.png
Variables: Yellow light time: 4 sec Reaction time: 0.4 sec Speed limit: 40 mph = 17.9 m/s Negative acceleration: -5 m/s^2 Width of intersection: about 18 m
Calculate and Diagram: GZ = Vity - w GZ = (17.9)(4) - 18 GZ = 53.6 m SZ = Vitr - (Vi^2)/(2a) SZ = (17.9)(0.4) - (17.9^2) / (2)(-5) SZ = 39.2 m
Doubling the speed limit makes a less safe intersection and causes a Dilemma Zone to form. It is extremely dangerous to you and others if you double the speed limit because you would be going twice as fast and it would take you much longer to stop, which is why the ticket is such a large fine. The Stop Zone changes more when speed is doubled because it is pushed back farther from the intersection, and the faster you go the harder it is to stop closer to the intersection.
Learning Outcomes:
What do you see/What do you think 11/3
What do you think?The yellow light should have been longer because the red car couldn't stop in time. It had to stop in the middle of the intersection. The green car is doing an illegal act because it is going through the red light.
Stop Zone/Go ZoneNovember 14th
Investigation:Friday, November 4th
3a.)Will automobile B be able to make it through the intersection?Yes, because automobile B cannot just come to a sudden stop with cars behind him3b.)Is automobile B in the go zone?yes B is, because B has no time to stop, or does not have enough distance left until the middle of the intersection.3c.)Would any automobile closer to the intersection that automobile A be in the Go Zone?Yes, because the closer you are with a yellow light, the more reason you have to continue through.3d.)Is automobile C in the go zone?No, and if C decided to continue, then they would
4a.)Is autopmobile E in the stop zone?Yes, because it is too far away from the yellow light to stop.4b.)Is automobile F in the stop zone? Explain your answer.No automobile F is in the Go zone, because they have enough room to stop.
PG 95-96 PART B
A-YesB-YesC-NoD-No
Go Zone/Stop Zone Notes:November 17th
ty (yellow light time)
w (width of intersection)
a (negative acceleration)
ty (yellow light time)
w (width of intersection)
a (negative acceleration)
tr (reaction time)
Go Zone Prediction/Actual Results:
Stop Zone Prediction/Actual Results:
Part B: Yellow Light Dilemma pg. 95November 18th1a. Automobiles A and D should stop, and B and C should go.2a. Automobiles E and F should stop, H has the choice, and G should go.3a. Automobiles J and L should stop, M has the choice, and K should go.4a. Intersection I has a distint STOP and GO Zone. Intersection II has an overlap that could be part of either the STOP or GO Zone. Intersection III has a Dilemma Zone.4b. Your choices are to either go or stop. It would be safe to do either because the zones are unclear.4c. Your choices are to either go or stop. Neither is safe because that area is neither a STOP Zone nor a GO Zone.4d. Intersection II has an Overlap Zone and Intersection III has a Dilemma Zonw.
Go Zone/Stop Zone EquationsNovember 18thGo Zone:
v = d/t
v = d/ty
v = (w + GZ) / ty
GZ = (v)(ty) - w
(The furthest distance at which you can go safely...where the Go Zone ends)
Stop Zone:
SZ = TSD
SZ = dr + dB
SZ = Vitr - (Vi)^2 / 2a
The closest position to the intersection in which you can brake safely...where the Stop Zone begins)
Checking Up Questions
November 18th
1. In this section, the spreadsheet is referred to as a model. What makes it a model?
A model is a mathematical equation to better understand a problem.
2. In your own words, describe what is meant by the GO Zone.
The GO Zone includes all positions where the automobile can safely proceed through the intersection when the light turns yellow.
3. In your own words, describe what is meant by the STOP Zone.
The STOP Zone includes all positions where the car can safely stop before reaching the intersection.
4. Describe what is meant by the Overlap Zone.
In the Overlap Zone, when the light turns yellow, the driver of the vehicle has the choice of either stopping or going through the intersection safely before the light turns red.
5. Describe what is meant by the Dilemma Zone.
The Dilemma Zone is a space between the STOP and GO Zones. In this region, a driver traveling the speed limit cannot safely stop before the intersection or pass through the intersction completely before the light turns red. Only occurs in a poorly designed intersection.
Active Physics Plus:
November 19th
1. Given a car approaching an intersection of width 25 m and yellow light time 3 seconds on a road of speed limit 45 mph (20 m/s) with a maximum deceleration of -5 m/s2 and a driver with reaction time .7 seconds. Diagram the intersection, calculate the Stop Zone and Go Zone, and decide if the intersection is safe or dangerous and explain why.
w = 25 m
ty = 3 s
Vi = 20 m/s
a = -5 m/s
tr = .7 s
--
GZ = (Vi)(ty) - w
GZ = (20)(3) - 25
GZ = 35 m
--
SZ = (Vi)(tr) - (Vi^2/(2a)
SZ = (20)(.7) - (20^2)/(2)(-5)
SZ = 54 m
2. Design 3 separate realistic and safe intersections. A realistic intersection has an overlap zone that is 10-30 m long. Re-compute the Stop Zones and Go Zones using the stop zone and go zone formulas then diagram the 3 safe intersections and photo them along with the calculations into your wiki. Check your intersections using the excel sheet to make sure its safe before you calculate the stop zone and go zone using the formulas.
3. Design 1 safe intersections for a cognizant driver of reaction time .5 sec and maximum deceleration of -6 m/s2. Choose the other 3 variables(speed limit, yellow light time and width of intersection) to make a safe and realistic intersection. A realistic intersection has an overlap zone that is 10-30 m long. You can use the excel sheet and do not have to use the manual formulas to calculate Stop Zone and Go Zone. Diagram them and list the 1 input variables under the photo of the diagram in your wiki.
4. Design 1 safe intersections for a fatigued driver with reaction time 2 seconds and maximum deceleration of -4 m/s2. Choose the other 3 variables(speed limit, yellow light time and width of intersection) to make a safe and realistic intersection. A realistic intersection has an overlap zone that is 10-30 m long. You can use the excel sheet and do not have to use the manual formulas to calculate Stop Zone and Go Zone. Diagram them and list the 5 input variables under the photo of the diagram in your wiki.
HW 10/9
1. The Go Zone would shrink because it would take longer to cross the intersection if it were wider.
2. The driver could change the velocity to increase the Go Zone.
3. The driver with bad brakes has to stop first, has a longer TSD, and has a Stop Zone pushed back farther away from the intersection.
4. The faster driver has a longer TSD and has a Stop Zone pushed back farther from the intersection.
5. The drunk driver has a longer TSD and has a Stop Zone pushed back farther from the intersection.
6. Speed affects the Stop Zone more because the variable "v" is used twice in the SZ equation. The Stop Zone is extended if you are going faster.
Go Zone/Stop Zone of a Real Intersection
November 13th
Intersection 5: Kinderkamack and Prospect Ave. in Woodcliff Lake
Yellow light time: 4 sec
Reaction time: 0.4 sec
Speed limit: 40 mph = 17.9 m/s
Negative acceleration: -5 m/s^2
Width of intersection: about 18 m
Calculate and Diagram:
GZ = Vity - w
GZ = (17.9)(4) - 18
GZ = 53.6 m
SZ = Vitr - (Vi^2)/(2a)
SZ = (17.9)(0.4) - (17.9^2) / (2)(-5)
SZ = 39.2 m
Double the speed limit:GZ = Vity - wGZ = (35.8)(4) - 18GZ = 125.2 mSZ = Vitr - (Vi^2)/(2a)SZ = (35.8)(0.4) - (35.8^2)/(2)(-5)SZ = 142.5 m
Doubling the speed limit makes a less safe intersection and causes a Dilemma Zone to form. It is extremely dangerous to you and others if you double the speed limit because you would be going twice as fast and it would take you much longer to stop, which is why the ticket is such a large fine. The Stop Zone changes more when speed is doubled because it is pushed back farther from the intersection, and the faster you go the harder it is to stop closer to the intersection.