Solving AP Mechanics Problem: Find DeltaTy for Vo & Minimal Time Interval

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SUMMARY

The discussion focuses on calculating the minimum yellow light duration, DeltaTy, for a vehicle approaching an intersection at various speeds (Vo). The problem requires evaluating DeltaTy for speeds of 8m/s, 11m/s, 18m/s, and 25m/s, as well as analyzing the behavior of DeltaTy as Vo approaches zero and infinity. The solution involves determining the stopping distance and time, and comparing it with the time required to coast through the intersection. The minimum yellow light duration is defined as the lesser of these two times.

PREREQUISITES
  • Understanding of kinematics, specifically equations of motion.
  • Familiarity with reaction time and its impact on vehicle stopping distance.
  • Knowledge of acceleration and deceleration concepts, particularly negative acceleration.
  • Ability to analyze physical scenarios using mathematical modeling.
NEXT STEPS
  • Calculate stopping distance using the formula: d = Vo * t + 0.5 * a * t^2.
  • Learn about the relationship between reaction time and stopping distance in driving scenarios.
  • Explore the implications of acceleration on vehicle dynamics during emergency stops.
  • Investigate the effects of varying speeds on traffic light timing and safety regulations.
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion, as well as traffic safety analysts and civil engineers involved in traffic light timing and vehicle dynamics.

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Homework Statement


Assume you are driving at the speed limit Vo. As you approach an intersection 22m wide, you see the light turn yellow. During your reaction time of .6s, you travel at a constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.4m/s2. Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it. (Suggestion: You may find it easier to do part (a) after part (b).)

a) Find the required time interval DeltaTy that the light should stay yellow in terms of Vo.
Evaluate answer for...
b) Vo = 8m/s
c) Vo = 11m/s
d) Vo = 18m/s
e) Vo = 25m/s

Evaluate your answer for...
f) Vo approaching zero
g) Vo approaching infinity
h) Describe pattern of variation of DeltaTy with Vo. Account for answers to parts (f) and (g) physically.
i) For what value of Vo would Deltaty be minimal?
j) What is the minimum time interval for part (i)?

Homework Equations


Probably the big 4 will be necessary in some form or another.

The Attempt at a Solution


I have no idea where to begin with this problem. I really don't even understand what it is asking and what is going on in the scenario.

I really appreciate any help.
Thanks guys.
 
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Start with part (b) as suggested. Find the stopping distance and time. Find the time to coast through the intersection from the distance from which you could stop. The light must stay yellow for the minimum of these two times.
 

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