Question 1: The electric current i (in A) as a function of the time t (in s) for

Question

Question 1:

The electric current i (in A) as a function of the time t (in s) for a certain circuit is given by: i = 4t – t2 . Find the average value of the current with respect to time for the first 4.0s. Then choose another interval and complete the calculations again.

Question 2:

The temperature T (in oC) recorded in a city during a given day approximately followed the curve of: T = 0.00100t4 -0.280t2 + 25.0 where t is the number of hours from noon (-12h< t < 12h). What was the average temperature during the day? Choose another interval (i.e. 2 or 3 hours) and complete the calculations again. The equation given is only accurate within the -12 h<t<12 h t time frame.

When you have completed this work post a response that clearly describes how this applet has increased your understanding of this concept. Additionally, give the answers for the intervals that you have chosen for each of the problems and explain the meaning of those answers in the context of each problem.

Explanation / Answer

1) i = 4t - t2

average current for the first 4 seconds = [i(4) - i(0)]/(4 - 0)

==> iavg = [4(4) - 42 - 4(0) + (0)2]/4

==> iavg = [0]/4 = 0

Hence average current for the first 4 seconds = 0 Amps

for the next 4 seconds average current = [i(8) - i(4)]/(8 - 4)

==> iavg = [4(8) - 82 - 4(4) + (4)2]/4

==> iavg = -32/4 = -8

Hence average current for the next 4 seconds = -8 Amps.

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