Question

The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e

Answer 1

All you need is the line of the secant from \(\color{black}{x=e}\) to \(\color{black}{x=2e}\).
(Because you want the average velocity, or the average rate of change.)

Answer 2

\(\color{black}{\displaystyle v_{\rm aver}=\frac{f(2e)-f(e)}{2e-e}}\)

Answer 3

But I'm confused as to what you do from there

Answer 4

Plug these into the function and evaluate.

Answer 5

so (ln(2e)-ln(e))/e ?

Answer 6

Yes, so far so good.

Answer 7

the choices are a.)ln2 b.)1/3e c.)ln2/e and d.) ln2/2

Answer 8

ln(a * b) = ln(a) + ln(b)

Answer 9

use this rule to simplify your expression

Answer 10

Or, alternatively, ln(a)-ln(b)=ln(a/b).

Answer 11

so would it be ln2/e?

Answer 12

Yup, there you go!

Answer 13

Thank you so much!!

Answer 14

yw