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Homework Help: Integration, where am i going wrong here?

  1. Nov 7, 2008 #1
    given,-

    [tex]\vec{a}[/tex][tex]_{x}[/tex]=6t[tex]^{2}[/tex]
    [tex]\vec{a}[/tex][tex]_{y}[/tex]=-4

    vector V(t=0)=0
    Vector R(t=0)=0

    1-the displacement from the 1st to the 3rd second
    2-the distance travelled fron the 2st to 3rd second
    ----------------------
    using integration,
    Vx=[tex]\int[/tex](ax)dt=2t[tex]^{3}[/tex]
    Vy=[tex]\int[/tex](ay)dt=-4t

    x=[tex]\int[/tex](Vx)dt=0.5t[tex]^{4}[/tex]
    y=[tex]\int[/tex](Vy)dt=-2t[tex]^{2}[/tex]

    then i found r(t=1)=(0.5,-4)
    and r(t=3)=(40.5,-18)

    delta(r)=42.38, which is the answer to question 1
    ----------------------
    now to find the distance travelled what i would like to do is integrate the vector V from 1 to 3, but once i get an answer for x and y, how do i connect them to get the scalar D, the distance he travelled?
     
    Last edited by a moderator: Nov 7, 2008
  2. jcsd
  3. Nov 7, 2008 #2
    can i apply pythagarus with x and y values?
     
    Last edited by a moderator: Nov 7, 2008
  4. Nov 7, 2008 #3
    That sounds right... the motion here is separable along x- and y-directions.
     
  5. Nov 8, 2008 #4
    sorrry, should read

    then i found r(t=1)=(0.5,-2)
    and r(t=3)=(40.5,-18)

    delta(r)=43.08, which is the answer to question 1,
    i did this by adding the sqared values of x and y and then square root on the answer, i think this gives me the displacement
     
    Last edited by a moderator: Nov 8, 2008
  6. Nov 8, 2008 #5
    thats fine, but what im looking for is the total distance travelled, not the displacemetn,,, so for example, if he travelled 10m X+, 7m X-, 20mY+,10mY-, what im looking for is 10+7+20+10, the total travelled, not sqrt(3^2+10^2),, problem here is its a complicated curve not straightforward, x then y. how do i calculate that? wont the integral just give me the displacement? also, how do i get a single scalar value, if i know that he walked 40m on X and 16 on y is the distance travelled43.08m?/ how else can i find it other thn pythagarus
     
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