1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ant crawls on a meter strick with acceleration

  1. Oct 10, 2004 #1
    I have a question ..an ant crawls on a meter strick with acceleration

    [tex]a(t)=t-1/2t^2[/tex]. After t seconds the ants intiial velocity is 2cm/s.

    The ants initial poistion is the 50cm mark. So ten [tex]\int_{a}^{b}f(t)dt[/tex]

    and [tex]v(t)=1/2t^2-1/6t^3+c[/tex] and because [tex]v(0)=2m/s[/tex]

    the equation is [tex]v(t)=1/2t^2-1/6t^3+2[/tex] and I did the same thing for

    the position function and came up with the final function for positon of

    [tex]s(t)=1/6t^3-1/24t^4+2t+50[/tex]....the problem is when asked what

    was the ants average velocity over the first 3 seconds of its journey. Using

    the [tex]\frac{1}{b-a}\int_{a}^{b}f(x)dx[/tex]

    theorem.......[tex]\frac{1}{3}\int_{0}^{3}t-\frac{1}{2}t^2dt[/tex] then I

    got [tex]\frac{1}{3}(\frac{9}{2}-\frac{27}{6})-\frac{1}{3}(0)[/tex]...Right

    here where the lower limit is [tex]0[/tex] I dicided that since

    [tex]v(0)=2[/tex] I would enter that value in for

    it....[tex]\frac{1}{3}(\frac{9}{2}-\frac{27}{6})-\frac{1}{3}(2)[/tex] but

    my answer came out to be [tex]-\frac{2}{3}[/tex] wich I wouldnt get if i

    averaged the regualr function with out using the theorem

    [tex]\frac{1}{b-a}\int_{a}^{b}f(x)dx[/tex]. Am I wrong?

    And the second qustion is the same question except.."over the first 6 seconds of its journy" so [tex][0,6][/tex]...the graph for this function goes down into the negatives...?
     
    Last edited: Oct 10, 2004
  2. jcsd
  3. Oct 10, 2004 #2

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why are you averaging the acceleration, instead of the velocity ?
     
  4. Oct 10, 2004 #3
    Hmm thats seems like a dumb mistake :uhh: I should be integrating the velocity
    ay?
    [tex]\frac{1}{b-a}\int_{a}^{b}f(x)dx[/tex]

    [tex]\frac{1}{3}\int_{0}^{3}\frac{1}{2}t^2-\frac{1}{6}t^3+2dt[/tex]


    [tex]\frac{1}{3}(\frac{57}{8})-\frac{1}{3}(0)[/tex] comes out to be

    [tex]2.375m/s[/tex]. Does anyone have any comment on that answer? I think its right from looking at the graph.
     
    Last edited: Oct 10, 2004
  5. Oct 10, 2004 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Use the basic definition of "average velocity". Since you already have the distance function, how far did the ant crawl between t= 0 and t= 3? Now divide the distance by 3 seconds.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Ant crawls on a meter strick with acceleration
Loading...