Final answer:
The total charge passing through the wire in the given time interval is 7.39 coulombs. A constant current of 0.87 amperes would transport the same charge in the same time interval.
Step-by-step explanation:
The charge passing through a cross-section of the wire can be found by integrating the current over the time interval. In this case, the current is given by the equation I=55A(0.65A/s^2)t^2. To find the charge passing through the wire, we need to evaluate the integral of this equation from t=0 to t=8.5s:
Q = ∫I dt = ∫55A(0.65A/s^2)t^2 dt = 7,39C
Therefore, the total charge passing through a cross section of the wire in the time interval between t=0 and t=8.5s is 7.39 coulombs.
To find the constant current that would transport the same charge in the same time interval, we can rearrange the equation Q = It to solve for I:
I = Q / t = 7.39C / 8.5s = 0.87A
Therefore, a constant current of 0.87 amperes would transport the same charge in the same time interval.