Question

The position of a particle on the x-axis at time t, t > 0, is s(t) = e^t with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 0 ≤ t ≤ In3?
a. 3
b. 2/ ln 3
c. 3/ ln 3
d. 3/ 2

Answer 1

average velocity is the rate of change in position over time.

find the final position of the particle at t=3s

Answer 2

@JFraser i still dont understand this

Answer 3

find the position of the particle when t = 3s

Answer 4

use the equation given \[s(t) = e^t\]to find the position when t = 3

Answer 5

I first must find the derivative of s(t) = s'(t) = v(t) right?

Answer 6

if you're looking for the \(average\) velocity, then no you don't need to find the derivative

Answer 7

you're going to use the data given to find the \(average\) rate of change over the given period of time, not the \(instantaneous\) velocity at a particular point

Answer 8

e^3?

Answer 9

@JFraser

Answer 10

that's the change in position of the particle after 3 seconds, \(e^3\) meters away from its starting point

Answer 11

do the same thing, but instead of 3 seconds, do \(ln(3)\) seconds

Answer 12

I just realized I misread the problem. It should have been \(ln(3)\) all along, not 3

Answer 13

e^ln 3? @JFraser

Answer 14

yes

Answer 15

now what do i do?

Answer 16

what's the value of \(e^{(ln(3))}\)

Answer 17

3 because e and ln cancel each other out? @JFraser

Answer 18

they are inverse functions, yes

Answer 19

so now you have the position after \(ln(3)\) seconds, 3 meters away

Answer 20

3 /ln 3

Answer 21

?

Answer 22

velocity = position/ distance right so 3 / ln 3. ln 3= distance

Answer 23

average velocity is the rate of change of position over time.

Now you have both of those values, the change in position is 3 meters, and the time is \(ln(3)\) seconds

Answer 24

so 3 / ln 3?

Answer 25

@JFraser

Answer 26

that's the one

Answer 27

Okay, thanks so much for the needed help! @JFraser

Answer 28

This answer is wrong @JFraser

Answer 29

I just got it wrong

Answer 30

if the question's asking for the average velocity, that's what it is.

Answer 31

I forgot that \(e^0\) isn't zero, it's one. So the change in position isn't 3 feet, it's 2 feet

Answer 32

2 ln /3

Answer 33

right? @JFraser

Answer 34

hello? @JFraser

Answer 35

@eliassaab can you help me?

Answer 36

I have to ride the bus back to campus and leave. I won't be back online until 4:00ish

Answer 37

*

Answer 38

\[
\frac {s(\ln 3)-s(0)}{\ln (3)-0}= \frac{3-1}{\ln 3}=\frac 2 {\ln 3}
\]

Answer 39

The answer is b

Answer 40

Thanks @eliassaab

Answer 41

YW

Answer 42

You can practice problems like this on my site
http://saab.org