The table provided contains time intervals and the corresponding velocities of a car in feet per second (ft/s). To find the total distance traveled along the twisty road, we need to calculate the approximate area under the velocity-time graph, using methods like the trapezoidal rule or rectangular approximations.

Would you like me to:

1. Use the trapezoidal rule for better accuracy?
2. Approximate using midpoint or left/right Riemann sums?

Let me know your preference! Here's how we could proceed: numpy as np

Time (s) and Velocity (ft/s) data from the table

time = np.array([0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]) velocity = np.array([0, 18, 47, 35, 39, 28, 30, 47, 30, 19, 39, 36, 33])

Trapezoidal Rule to calculate the distance traveled

distance = np.trapz(velocity, time) distanceUsing the trapezoidal rule, the total distance traveled along the twisty road is approximately 3845 feet.

Would you like a detailed breakdown of the calculations or clarification on the method? Here are some follow-up questions to extend the discussion:

1. Would you like to see the result using a different numerical approximation (e.g., midpoint or left/right Riemann sums)?
2. Should we explore how the trapezoidal rule works step by step?
3. Do you want to calculate the average velocity during this trip?
4. Would you like to discuss how changing time intervals might affect the accuracy of the calculation?
5. Should we convert the velocity into other units, such as miles per hour?

Tip: The trapezoidal rule is especially accurate for smoothly varying data but less so for irregular data points.