Question

The position of a particle on the x-axis at time t, t >0, is ln(t). The average velocity of the particle for 1 <= t <= e is.

A. (1/e) - 1
B. 1/(e - 1)
C. e
D. e - 1
Please show work

Answer 1

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).

Answer 2

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