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The velocity of a car over five hours is given by v(t) = 60 ln(t + 1), 0 < t < 5 in kilometers per hour. What is the total dista
Question
The velocity of a car over five hours is given by v(t) = 60 ln(t + 1), 0 < t < 5
in kilometers per hour. What is the total distance traveled from t = 0 to t = 5?
Round your answer to the nearest whole number and do not include units.
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Mathematics
3 years
2021-07-28T14:13:17+00:00
2021-07-28T14:13:17+00:00 1 Answers
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Answer:
345
Step-by-step explanation:
The velocity of a car over five hours is given by:
And we want to find the total distance traveled from t = 0 to t = 5.
Recall that distance is the integral of the absolute value of the velocity function. Since we want to find the total distance traveled from t = 0 to t = 5, our limits of integration are t = 0 and t = 5. Hence:
Since v(t) ≥ 0 for all t in the interval [1, 5], we can remove the absolute value. Use a calculator: