Results 1 to 7 of 7

Math Help - Displacement, distance and average velocity

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    57

    Displacement, distance and average velocity

    Hi,
    I was having a bit of trouble with this question.

    For a) I found -3/1/3 for the displacement be evaluating the definite integral.

    For b) I found 32/2/3 to be the distance travelled using the fact the below 4 the curve is negative and above 4 the curve is positive.
    I would be great if some else could do these to and see if they get similar answers as I'm not sure what answers to expect.

    For c) using the Mean Value Theorem f ave=1/b-a integral b a f(x) dx, I found the average velocity to be -6 but I'm not sure if I used the correct a and b values. I made a=1 and b=4 (as this is were the curve cuts the x axis)

    If someone could show me how to do this it would be a great help.

    Thanks,
    Daddy_Long_Legs
    Attached Thumbnails Attached Thumbnails Displacement, distance and average velocity-question-5.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Daddy_Long_Legs View Post
    Hi,
    I was having a bit of trouble with this question.

    For a) I found -3/1/3 for the displacement be evaluating the definite integral.

    For b) I found 32/2/3 to be the distance travelled using the fact the below 4 the curve is negative and above 4 the curve is positive.
    I would be great if some else could do these to and see if they get similar answers as I'm not sure what answers to expect.

    For c) using the Mean Value Theorem f ave=1/b-a integral b a f(x) dx, I found the average velocity to be -6 but I'm not sure if I used the correct a and b values. I made a=1 and b=4 (as this is were the curve cuts the x axis)

    If someone could show me how to do this it would be a great help.

    Thanks,
    Daddy_Long_Legs
    a) is correct.

    b) is correct.

    c) Average velocity = displacement/time = ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    57
    Thanks for the help mr fantastic,

    I'm not sure what you mean by Average velocity = displacement/time =. Doing this means the average velocity would be equal to -3/1/3 / 5 which is would be -2/3.

    I was wondering if I could do this using the Mean Value Theorem? Its just I'm not sure how to find the definite integral to evaluate as Iím sure I have to go about the problem this way.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Daddy_Long_Legs View Post
    Thanks for the help mr fantastic,

    I'm not sure what you mean by Average velocity = displacement/time =. Doing this means the average velocity would be equal to -3/1/3 / 5 which is would be -2/3.

    I was wondering if I could do this using the Mean Value Theorem? Its just I'm not sure how to find the definite integral to evaluate as I’m sure I have to go about the problem this way.
    The average value of the function f(t) over the interval [a, b] is defined to be \frac{\int_a^b f(t) \, dt}{b - a}.

    When f(t) is velocity the above definition reduces to the expression I used (which is the standard definition of average velocity, by the way).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2009
    Posts
    57
    mr fantastic

    I was using this formula when I found the answer -6, but this was using a=1 and b=4, (b=4 because of the fact that the curve cut the x-axis at 4.)

    I saw a similar problem with the function f=t-ľ*t^2 over the interval of 0=<t<=6 and the fact that this graph intercepts the x-axis at 4 a=0 and b=4. Not b=6 as what you are suggesting.

    I should have said that this was the problem I was having with the question.

    Using a=1 and b=6 gives an answer of -2/3 and using a=1 and b=4 gives an answer of -6.
    I'm not sure that if the curve cuts the x-axis this needs to be taken into account as I have seen it possibly has in a similar question but Iím unsure.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Daddy_Long_Legs View Post
    mr fantastic

    I was using this formula when I found the answer -6, but this was using a=1 and b=4, (b=4 because of the fact that the curve cut the x-axis at 4.)

    I saw a similar problem with the function f=t-ľ*t^2 over the interval of 0=<t<=6 and the fact that this graph intercepts the x-axis at 4 a=0 and b=4. Not b=6 as what you are suggesting.

    I should have said that this was the problem I was having with the question.

    Using a=1 and b=6 gives an answer of -2/3 and using a=1 and b=4 gives an answer of -6.
    I'm not sure that if the curve cuts the x-axis this needs to be taken into account as I have seen it possibly has in a similar question but Iím unsure.
    average velocity is determined for the entire time interval, as stated in the original question ...

    v_{avg} = \frac{\Delta x}{\Delta t} = \frac{\int_1^6 v(t) \, dt}{6-1}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2009
    Posts
    57
    mr fantastic and skeeter

    Okay, thanks for the help. It seems that the similar question I mentioned may have been to find the average velocity over 0 to 4 seconds but I can't be sure.

    I think using the interval seems making a=1 and b=6 seems like the most reasonable thing to do thing to do.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 10th 2011, 02:04 PM
  2. Velocity from displacement
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 14th 2010, 10:16 PM
  3. Replies: 2
    Last Post: December 7th 2009, 06:15 AM
  4. velocity - displacement help
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 27th 2009, 03:34 AM
  5. Velocity, Displacement, Distance
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 12th 2009, 02:20 PM

Search Tags


/mathhelpforum @mathhelpforum