Question

Given the position function

Answer 1

Given the position function,between t = 0 and t = 15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.

Answer 2

\[s(t)= \frac{ t^3 }{ 3 } - \frac{ 12t^2 }{ 2 } + 36t\]

Answer 3

@ganeshie8 @e.mccormick @Nnesha @Loser66 @undeadknight26 @Zale101 @DanJS @EclipsedStar @sleepyjess

Answer 4

s(t) is the position equation. Take the first derivative to get the velocity equation so we can find the critical points and then test numbers to see where the particle is moving to the right.

Answer 5

When you test values near the critical values, you can be able to know which one indicates that the particle is moving to right or left. If you plug in a value and the answer is positive, then it moves to the right.

So, first things first. Take the first derivative to get the velocity.

Answer 6

\[t^2-12t+36\]

Answer 7

@Zale101

Answer 8

right... idk wht to do here

Answer 9

this means?

Answer 10

okay so how do we test the #s...plug in?

Answer 11

@Zale101 t^2 - 12t +36 , not +12 t, that makes your mistake to have the negative time

Answer 12

Omg, thank you very much!! <3 the mistake was silly >.<

Answer 13

t^2-12t+36=0
(t-6)(t-6)=0
t=6

Answer 14

Let's do this one more time. You're seeing what i'm trying to do @familyguymath ?
Setting the velocity to zero and solve for t, the number i get for t is the critical point.

Answer 15

yes i understand

Answer 16

and im not just saying that i get that we r supposed to find the critical pt

Answer 17

The position has an interval between 0 and 15 correct? That means that we test any numbers that after and before 6 ONLY values that is in the interval.

Answer 18

right

Answer 19

picky any number between zero and 6 and then plug it back to the velocity equation
t^2-12t+36=y
See what value you'll get. Can you do this part?

Answer 20

pick*

Answer 21

i plug in 3 and i got 9

Answer 22

You got positive 9, that means that the particle is moving to the right.

Answer 23

Test any numbers after 6 and see what values you get.

Answer 24

i plugged in 8 and i got 4

Answer 25

@Zale101

Answer 26

It's also positive, that means that the interval that has the particle going to the right is [0,15]

Answer 27

hese r the answers
a. 0 < t < 6
b. 5 < t < 15
c. t > 15
d. The particle always moves to the right.

Answer 28

*these

Answer 29

I'd say d is correct because we took the derivative correctly, we found out the critical point by simply factoring, we tested number between the interval that's after 6 and before 6. B is definitely wrong, because as you can see, the critical point is not even there.

a is not correct because when you did 8, we got positive 4. C is definitely wrong, because there's an interval between 0 and 15 it's saying 15 and positive infinity is the interval which is wrong.

Answer 30

can u help me on another problem?