Question

Check my answer?

Answer 1

Position: x(t) = 3t - ln(4t+1)
a) find the average velocity in the first 3 seconds
b) find the instantaneous velocity at 1/2 second
c) find the acceleration at 1/2 second

Answer 2

my answers:
a) (9 - ln(13))/3
b) 5/3
c) -16/9

Answer 3

@sweetburger do you know this? :)

Answer 4

Average of any physical quantity is defined over an interval of time.

Average velocity=(x(3)-x(0))/(3-0)

Answer 5

x(3) = 9 - ln(13) and x(0) = 0

Answer 6

Right?

Answer 7

To get the instantaneous velocity u need to differentiate x(t) with respect to time and then put t=1/2 sec

Answer 8

I don't plug it into the derivative?

Answer 9

yes - i was wrong - find derivative then plug in t = 1/2

Answer 10

That's what I did... do you guys see the answers I got?
a) (9 - ln(13))/3
b) 5/3
c) -16/9

Answer 11

And finally after differentiating x(t) with respect to time u will get v(t) .

All u need is to differentiate v(t) with respect to time and plug t=1/2

Answer 12

to find the acceleration find the second derivative then plug in t -= 1/2

Answer 13

That's what I did :/ did I do it wrong or are my answers right? lol

Answer 14

v(t) = 3 - [4 / (4t + 1)]

Answer 15

5/3 is correct

Answer 16

what about the ln part?

Answer 17

derivative of ln x is 1/x

Answer 18

Is this for part a ?

Answer 19

Was my answer for part a correct?

Answer 20

no part b

Answer 21

yes

Answer 22

oh! :)

Answer 23

so which of my answers was wrong?

Answer 24

I havent checked c yet a and b are correct

Answer 25

what did you get for the second derivative
a(t) = what?

Answer 26

- the acceleration

Answer 27

-16/(4t+1)^2

Answer 28

right
so at t = 1/2 we get -16/9

Answer 29

Lol xD thanks

Answer 30

yea good work