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The velocity of a car accelarating from a stop light is shown in the graph below. Use the graph to determine an estimate of the distance traveled during the first 40 seconds of driving. Use 8 midpoint approximating rectangles to get the most accurate approximation possible. (Note: t is measured in seconds, and vis measured in km/hr.) (Round your answer to the nearest hundredth km.) km 100 (km/hr) 90 80 70 60 50 40 30 20 10 10 20 30 t (sec) 40

The velocity of a car accelarating from a stop light is shown in the graph below. Use the graph to determine an estimate of the distance traveled during the first 40 seconds of driving. Use 8 midpoint approximating rectangles to get the most accurate approximation possible. (Note: t is measured in seconds, and vis measured in km/hr.) (Round your answer to the nearest hundredth km.) km 100 (km/hr) 90 80 70 60 50 40 30 20 10 10 20 30 t (sec) 40

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Velocity and Distance Approximation** The velocity of a car accelerating from a stop light is shown in the graph below. Use the graph to determine an estimate of the distance traveled during the first 40 seconds of driving. Use 8 midpoint approximating rectangles to get the most accurate approximation possible. (Note: \(t\) is measured in seconds, and \(v\) is measured in km/hr.) *(Round your answer to the nearest hundredth km.)* **Graph Description:** - The horizontal axis (x-axis) represents time \(t\) in seconds, ranging from 0 to 40 seconds. - The vertical axis (y-axis) represents velocity \(v\) in km/hr, from 0 to 100 km/hr. - The graph shows a blue curve representing the velocity of the car. It starts at approximately 10 km/hr at \(t = 0\) and increases, curving upwards, reaching close to 100 km/hr at \(t = 40\) seconds. To approximate the distance traveled, divide the time interval [0, 40 seconds] into 8 equal subintervals, each of 5 seconds. Find the midpoint of each subinterval, use the velocity at these midpoints to construct rectangles, and calculate the sum of their areas to estimate the distance traveled.
Transcribed Image Text:**Velocity and Distance Approximation** The velocity of a car accelerating from a stop light is shown in the graph below. Use the graph to determine an estimate of the distance traveled during the first 40 seconds of driving. Use 8 midpoint approximating rectangles to get the most accurate approximation possible. (Note: \(t\) is measured in seconds, and \(v\) is measured in km/hr.) *(Round your answer to the nearest hundredth km.)* **Graph Description:** - The horizontal axis (x-axis) represents time \(t\) in seconds, ranging from 0 to 40 seconds. - The vertical axis (y-axis) represents velocity \(v\) in km/hr, from 0 to 100 km/hr. - The graph shows a blue curve representing the velocity of the car. It starts at approximately 10 km/hr at \(t = 0\) and increases, curving upwards, reaching close to 100 km/hr at \(t = 40\) seconds. To approximate the distance traveled, divide the time interval [0, 40 seconds] into 8 equal subintervals, each of 5 seconds. Find the midpoint of each subinterval, use the velocity at these midpoints to construct rectangles, and calculate the sum of their areas to estimate the distance traveled.
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