anonymous
  • anonymous
Find the time intervals for v(t) = t^2 - 9t + 18 when the particle is a.going faster b.slowing down
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
so iv go a. (4.5 , infinity) b. (-infinity , 4.5) but apparently their is 2 intervals for each
ganeshie8
  • ganeshie8
see if the graph helps |dw:1438632617992:dw|
ganeshie8
  • ganeshie8
I think you also need to look at the points where the velocity is becoming 0 (x intercepts)

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anonymous
  • anonymous
yes thats what i was thinking but that wouldn't allow 2 intervals for each
ganeshie8
  • ganeshie8
|dw:1438633001610:dw|
Astrophysics
  • 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.
Astrophysics
  • Astrophysics
But ganeshies graph is perfect to, as you can tell easily with it xD
anonymous
  • anonymous
yeah i used the acceleration graph to find my answer initially, to be honest i still don't know why its wrong
ganeshie8
  • 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.
freckles
  • freckles
speed=|velocity||dw:1438633412827:dw| you could reflect the part that is below the graph about the x-axis
freckles
  • freckles
below the graph I mean below the x-axis
ganeshie8
  • ganeshie8
That speed graph looks so much clear!
anonymous
  • anonymous
okay so then it would be a.(3,4.5)U(6,infinity) b.(-infinity,3)U(3,6)
anonymous
  • anonymous
is that right?
Astrophysics
  • Astrophysics
Mhm
freckles
  • freckles
well
freckles
  • freckles
there is one endpoint just a tad off
anonymous
  • anonymous
where are you getting the eight from ?
freckles
  • freckles
\[\text{ "okay so then it would be } \\ a.(3,4.5) \cup (6,\infty) \\ b.(-\infty,3) \cup (\color{red}{3},6) \\ \text{ " } \\ \text{ I think this 3 is a type-o}\]
anonymous
  • anonymous
yes it is i ment (4.5 , 6)
freckles
  • freckles
cool stuff then
ganeshie8
  • ganeshie8
|dw:1438633971759:dw|