Question

The velocity of a particle is given by the function
v(t)=3t+6 and the position at t=2 is 3.
Is the particle moving to the let or right at t=2?

Answer 1

I am still having problems with particle motion.
I believe I am suppose to figure out v(2)
if so, then v(2)=12 and the particle is moving right since v(2)>0

Answer 2

not sure that is correct

Answer 3

I also, have to figure out the position of the particle, s(t), for any time t>0 (or equal to zero)

Answer 4

thats perfect !
positive velocity => particle is moving in the increasing direction of assumed position direction

Answer 5

for the second part I did 3t+6>0 t>-2 (also include equal sign)
this second part I believe I did incorrect

Answer 6

use below for position function s(t) :

\[\large s(t) - s(2) = \int \limits_{2}^tv(t) dt\]

Answer 7

ok this will help me find s(t)?

Answer 8

I have to leave in a couple of minutes but I will finish this later.
I just need to make sure I am setting up the rest of them, I can solve them later when I have more time.
I also, have to find where the particle changes direction. So if I determine s(t) then I can set that equal to zero to solve for t. correct?
then my last part is asking for the total distance traveled by the particle for t=1 and t=4.
that is just an integral from 1 to 4 using s(t) dt, correct?

Answer 9

yes take the integral since we know s(2) already...

for determining when the particle changes it direction, we may simply set v(t) = 0

Answer 10

ok thanks, gotta go, I will look at this later today. :)

Answer 11

okie have a nice day :)