(Treat as a kinematics problem) You are on a team that designs driver assist software for next generation cars. Currently, you are working on the following question: if you are driving with speed v, and the traffic light a distance d ahead of you turns yellow, what shall the car do, brake and come to a complete stop right at the intersection, or speed up and make it through the intersection just before the light turns red. The time duration for the yellow light is ty. Cars, intersections are all modeled as being point-like; the moment the light turns yellow is designated as t = 0 s. What is the critical distance where the car needs to take action (breaking or

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**Educational Content on Kinematics and Driver Assistance Systems**

1. **Scenario Context**
   - You are on a team developing driver assist software for next-generation cars. Your task involves examining a scenario where a vehicle approaches a traffic light that turns yellow. The challenge is to determine whether the car should stop or accelerate through the intersection before the light turns red. The time duration for the yellow light is \( t_y \), and all vehicles and intersections are simplified as point-like objects. The moment the light turns yellow is set as \( t = 0 \).

2. **Questions for Analysis**

   a) **Critical Distance for Action**
      - Determine the crucial distance at which the vehicle must decide to either brake or accelerate to avoid crossing the intersection on a red light.

   b) **Unacceptable Scenario Graph**
      - Create a position-velocity-acceleration-time graph for the scenario where no appropriate action (braking or accelerating) is taken, resulting in running the red light.

   c) **Acceptable Scenario Graphs**
      - Develop position-velocity-acceleration-time graphs for acceptable responses:
        - **Braking**: Slowing down to stop before the intersection.
        - **Accelerating**: Speeding up to clear the intersection before the light changes to red.

   d) **Required Acceleration for Crossing**
      - For accelerating, calculate the required acceleration to pass through the light just as it turns red. Also, evaluate the moment of crossing during the light cycle.

   e) **Required Deceleration for Stopping**
      - For braking, determine the necessary deceleration to come to a full stop at the intersection. Also, find the exact stopping time relative to the light cycle. 

These exercises are designed to test and enhance understanding of kinematics in a real-world application, focusing on safety and efficiency in urban traffic scenarios.
Transcribed Image Text:**Educational Content on Kinematics and Driver Assistance Systems** 1. **Scenario Context** - You are on a team developing driver assist software for next-generation cars. Your task involves examining a scenario where a vehicle approaches a traffic light that turns yellow. The challenge is to determine whether the car should stop or accelerate through the intersection before the light turns red. The time duration for the yellow light is \( t_y \), and all vehicles and intersections are simplified as point-like objects. The moment the light turns yellow is set as \( t = 0 \). 2. **Questions for Analysis** a) **Critical Distance for Action** - Determine the crucial distance at which the vehicle must decide to either brake or accelerate to avoid crossing the intersection on a red light. b) **Unacceptable Scenario Graph** - Create a position-velocity-acceleration-time graph for the scenario where no appropriate action (braking or accelerating) is taken, resulting in running the red light. c) **Acceptable Scenario Graphs** - Develop position-velocity-acceleration-time graphs for acceptable responses: - **Braking**: Slowing down to stop before the intersection. - **Accelerating**: Speeding up to clear the intersection before the light changes to red. d) **Required Acceleration for Crossing** - For accelerating, calculate the required acceleration to pass through the light just as it turns red. Also, evaluate the moment of crossing during the light cycle. e) **Required Deceleration for Stopping** - For braking, determine the necessary deceleration to come to a full stop at the intersection. Also, find the exact stopping time relative to the light cycle. These exercises are designed to test and enhance understanding of kinematics in a real-world application, focusing on safety and efficiency in urban traffic scenarios.
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