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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Đan Thu 3 years 2021-07-28T14:13:17+00:00 1 Answers 39 views 0

Answers ( )

    0
    2021-07-28T14:14:50+00:00

    Answer:

    345

    Step-by-step explanation:

    The velocity of a car over five hours is given by:

    \displaystyle v(t)=60\ln(t+1),\, 0 \leq t \leq 5

    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:

    \displaystyle D=\int_0^5 |\underbrace{60\ln(t+1)}_{v(t)}|\, dt

    Since v(t) ≥ 0 for all t in the interval [1, 5], we can remove the absolute value. Use a calculator:

    \displaystyle D=60\left(6\ln(6)-5)=345.0334...\approx 345

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