Explanation:
To find the average velocity of the particle over the interval [1, e], we need to calculate the net displacement divided by the time interval.
Given the position function x(t) = ln(t), let's find the displacement by evaluating x(e) and x(1):
x(e) = ln(e) = 1
x(1) = ln(1) = 0
So, the net displacement is 1 - 0 = 1.
The time interval is e - 1.
Therefore, the average velocity is:
average velocity = (net displacement) / (time interval)
average velocity = 1 / (e - 1)
The correct answer is B. 1/(e - 1).