34.7. Problems

Try these first

1. 1.

   Define what a car-following model is.

   Hint

   What does it help us understand about traffic?

2. 2.

   What is the sensitivity coefficient (α)?

   Hint

   Think about the driver's reaction to vehicle speed changes.

3. 3.

   What does the sensitivity coefficient (α) measure?

   • Responsiveness to speed changes
   • Distance headway measures
   • Number of vehicles on the road

   Hint

   Consider how quickly drivers can react to changes in speed.

4. 4.

   True or False: A following vehicle has no reaction time.

   • True
   • False

   Hint

   Think about how long it takes to notice changes.

5. 5.

   Given a leader vehicle that accelerates by 2 m/s² for 3 seconds, calculate the position of the leader at t = 3 seconds. If a following vehicle starts with a speed of 15 m/s and maintains a reaction time of 1 second, what speed will it be travelling at t = 3 seconds?

   Hint

   First calculate the lead vehicle's position before determining the following vehicle's speed.

6. 6.

   Analyze the behavior of the following vehicle if the leader decelerates suddenly from 20 m/s to 10 m/s in 2 seconds. Calculate the new speed and position of the following vehicle assuming α = 10.

   Hint

   Break the problem down into calculating the speed reduction and reaction time adjustments.