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14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period. v (km/h) 120 80 40 0 10 지 20 30 t (seconds)

14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period. v (km/h) 120 80 40 0 10 지 20 30 t (seconds)

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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**14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period.** **Graph Description:** - The graph depicts the velocity (v) of a car in kilometers per hour (km/h) over time (t) in seconds. - The horizontal axis represents time, ranging from 0 to 30 seconds. - The vertical axis represents velocity, ranging from 0 to 120 km/h. - The curve starts at the origin (0,0), indicating the car is at rest initially. - The curve gradually rises, indicating an increase in velocity, reaching 120 km/h at 30 seconds. - The shape of the curve suggests a non-linear acceleration, possibly quadratic, due to its upward curvature. **Estimation of Distance:** To estimate the distance traveled, calculate the area under the velocity-time graph from 0 to 30 seconds. This area represents the total distance covered. The graph's shape suggests this area may be calculated using integration methods or approximated if a specific function is known.
Transcribed Image Text:**14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period.** **Graph Description:** - The graph depicts the velocity (v) of a car in kilometers per hour (km/h) over time (t) in seconds. - The horizontal axis represents time, ranging from 0 to 30 seconds. - The vertical axis represents velocity, ranging from 0 to 120 km/h. - The curve starts at the origin (0,0), indicating the car is at rest initially. - The curve gradually rises, indicating an increase in velocity, reaching 120 km/h at 30 seconds. - The shape of the curve suggests a non-linear acceleration, possibly quadratic, due to its upward curvature. **Estimation of Distance:** To estimate the distance traveled, calculate the area under the velocity-time graph from 0 to 30 seconds. This area represents the total distance covered. The graph's shape suggests this area may be calculated using integration methods or approximated if a specific function is known.
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