32.5 is the correct answer
answer and explanation are in the picture.
Step-by-step explanation:
as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.
v(t) = 60×ln(t + 1)
V(t) = 60 × integral(ln(t + 1)) between 0 and 5.
integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C
V(t) = 60 × ((t + 1)ln(t + 1) - t + C)
the distance traveled between t = 0 and t = 5 is then
60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =
= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =
= 60×(5.750556815... + C) - 60×C =
= 60×5.750556815... = 345.0334089... ≈ 345 km
