Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Bladerunner1122 Group Title

Question help please

  • one year ago
  • one year ago

  • This Question is Closed
  1. Bladerunner1122 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    • one year ago
    1 Attachment
  2. SithsAndGiggles Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    a) You can see that 0 ≤ t ≤ 40, so dividing this interval into four sub-intervals isn't too difficult. You get the following four intervals: \[[0,10], [10,20], [20,30], [30,40].\] So, the length of each sub-interval is 10. The midpoints of these intervals are 5, 15, 25, and 35, respectively. \[\int_0^{40}v(t)\;dt\approx\frac{1}{10}\left(v(5)+v(15)+v(25)+v(35)\right)\]

    • one year ago
  3. Bladerunner1122 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    How do I do b c d?

    • one year ago
  4. SithsAndGiggles Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    b) Here you have to look for when v(t) is increasing and decreasing. I presume you know about the first derivative test, and that acceleration, a(t), is the derivative of velocity, v(t). When a(t) < 0, v(t) is decreasing; when a(t) > 0, v(t) is increasing. So, when velocity changes from increasing to decreasing (or decreasing to increasing), this would indicate a(t) = 0 at some t. For example, one instance in this situation is over [0,15]. Over [0,10], it looks like v(t) is increasing (in general; it's completely possible that velocity is oscillating), but when t = 15, v(t) drops down from 9.5 to 7.0 mpm. The increase-decrease indicates at least one instance of zero acceleration. If you take a look at the tick marks on the table, it looks like someone has already pointed out where the sign changes of v(t) occur.

    • one year ago
  5. SithsAndGiggles Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    c) Velocity is given by the function \[f(t) = 6+\cos{\frac{t}{10}}+\sin{\frac{7t}{40}}.\] To find the acceleration at t = 23, you must find f '(23), since f '(t) = a(t).

    • one year ago
  6. SithsAndGiggles Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    d) If f(t) is a velocity function, then average velocity over [a,b] would be given by \[v_{avg} = \frac{f(b)-f(a)}{b-a}\]

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.