## anonymous one year ago Find the time intervals for v(t) = t^2 - 9t + 18 when the particle is a.going faster b.slowing down

1. anonymous

so iv go a. (4.5 , infinity) b. (-infinity , 4.5) but apparently their is 2 intervals for each

2. ganeshie8

see if the graph helps |dw:1438632617992:dw|

3. ganeshie8

I think you also need to look at the points where the velocity is becoming 0 (x intercepts)

4. anonymous

yes thats what i was thinking but that wouldn't allow 2 intervals for each

5. ganeshie8

|dw:1438633001610:dw|

6. Astrophysics

You could use acceleration to your advantage just look at where the acceleration is increasing, and then you can use similar way to determine where it's decreasing as the sign will be opposite of the velocity.

7. Astrophysics

But ganeshies graph is perfect to, as you can tell easily with it xD

8. anonymous

yeah i used the acceleration graph to find my answer initially, to be honest i still don't know why its wrong

9. ganeshie8

From the graph it is clear that the particle's "speed" is decreasing in the interval $$(-\infty, ~3)$$. Then the particle has changed its direction, and its "speed" starts increasing in the interval $$(3,~4.5)$$. After that, the particle slows down, its "speed" starts decreasing in the interval $$(4.5, ~6)$$ and becomes $$0$$ at $$t=6$$. For the rest, the speed keeps increasing.

10. freckles

speed=|velocity||dw:1438633412827:dw| you could reflect the part that is below the graph about the x-axis

11. freckles

below the graph I mean below the x-axis

12. ganeshie8

That speed graph looks so much clear!

13. anonymous

okay so then it would be a.(3,4.5)U(6,infinity) b.(-infinity,3)U(3,6)

14. anonymous

is that right?

15. Astrophysics

Mhm

16. freckles

well

17. freckles

there is one endpoint just a tad off

18. anonymous

where are you getting the eight from ?

19. freckles

$\text{ "okay so then it would be } \\ a.(3,4.5) \cup (6,\infty) \\ b.(-\infty,3) \cup (\color{red}{3},6) \\ \text{ " } \\ \text{ I think this 3 is a type-o}$

20. anonymous

yes it is i ment (4.5 , 6)

21. freckles

cool stuff then

22. ganeshie8

|dw:1438633971759:dw|