anonymous
  • anonymous
A Particle travels on the x-axis so its velocity at time t is given by v(t)=1/2-cos(t) meters per second, where t is between 0 and 2pi, inclusive. A. For what values of t is the particle moving to the right? B. If the particle starts at x=3, what is the final position of the article? C. What is the total distance traveled by the particle? D. When t=pi/4, is the speed of the particle increasing or decreasing?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
to the right where the velocity is postive
anonymous
  • anonymous
|dw:1330660592899:dw|
anonymous
  • anonymous
moves to the right for \[\frac{\pi}{3}

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anonymous
  • anonymous
anonymous
  • anonymous
\[x(t)=\frac{1}{2}t-\sin(t)+c\] find c by \[3=\frac{1}{2}\times 3-\sin(0)+c=3\] \[c=3\] so \[x(t)=\frac{1}{2}t-\sin(t)+3\]
anonymous
  • anonymous
another typo, meant \[3=\frac{1}{2}\times 0-\sin(0)+c=3\]
anonymous
  • anonymous
so final postion is \[x(2\pi)=\frac{1}{2}\times 2\pi-\sin(2\pi)+3=\pi+3\]
anonymous
  • anonymous
What is the reasoning, I mean, how did you get to that algebraic setup?
anonymous
  • anonymous
total distance is a pain, because it moves to the left, then to the right, then to the left. you have to calculate the distance 3 times and add
anonymous
  • anonymous
i took the anti derivative of the velocity to get the distance. not really algebra
anonymous
  • anonymous
ohh
anonymous
  • anonymous
i should say "position" not distance
anonymous
  • anonymous
Okay, and total distance you need to take the abs value of the 3 parts?
anonymous
  • anonymous
yes from t = 0 to t = pi/3 from pi/3 to 5pi/3 from 5pi/3 to 2 pi what a pain
anonymous
  • anonymous
no worries, I can do that
anonymous
  • anonymous
What about part D?
anonymous
  • anonymous
that is why the first question asked about moving left and moving right
anonymous
  • anonymous
but speed increasing means, BOTH velocity and acceleration positive right?
anonymous
  • anonymous
When t=pi/4, is the speed of the particle increasing or decreasing? that is easier. take the derivative of the velocity to get acceleration. replace t by pi/4
anonymous
  • anonymous
if it is positive, increasing, if it is negative, decreasing
anonymous
  • anonymous
Just acceleration positive?
anonymous
  • anonymous
yes
anonymous
  • anonymous
you can speed up in reverse
anonymous
  • anonymous
oh wow this is like physics
anonymous
  • anonymous
yea i understand it when thinking about a car, sort of
anonymous
  • anonymous
something like that i guess. actually that is where this stuff comes from
anonymous
  • anonymous
Thanks for all the help!
anonymous
  • anonymous
yw, hope you are good from here because i surely don't want to do all that compution although the last part you can do in your head. derivative of - cosine is sine, and sine pi/4 is positive
anonymous
  • anonymous
Yup no worries, it's the concepts that are most important. I think I might buy the barron's book for prep since they have the solucions in there as well.

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