Results 1 to 2 of 2

Math Help - Ap Question 2003

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    1

    Ap Question 2003

    A particle moves along the x-axis so that its velocity at time t is given by v(t)=-(t+1)sin(t^2/2). During the time interval 0<t<3 or equal to t, what is the total distance between the particle and the origin? At t = 0 , the particle is at position x = 1.

    The answer is x(0)+ antideriviative of v(t) from 0 to the square of 2pi.

    Please explain why.

    x(0) must be where you start from and the total distance traveled is 4.334. But I'm still confused on why the distance is 2.265.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,892
    Thanks
    683
    Quote Originally Posted by darleneflorio View Post
    A particle moves along the x-axis so that its velocity at time t is given by v(t)=-(t+1)sin(t^2/2). During the time interval 0<t<3 or equal to t, what is the total distance between the particle and the origin? At t = 0 , the particle is at position x = 1.

    The answer is x(0)+ antideriviative of v(t) from 0 to the square of 2pi.

    Please explain why.

    x(0) must be where you start from and the total distance traveled is 4.334. But I'm still confused on why the distance is 2.265.
    total distance traveled is not the same as distance from the origin.

    if you walk 10 miles away from your house (the origin) and walk 9 miles back, the total distance you traveled is 19 miles ... that is not the distance you end up from your house, is it?

    distance from the origin is x(3) - 0 = x(3)

    x(3) = x(1) + \int_1^3 v(t) \, dt

    because the FTC says ...

    x(3) - x(1) = \int_1^3 v(t) \, dt
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2003 Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: July 17th 2010, 05:19 AM
  2. 2003 AP BC Calculus MC Questions
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 4th 2010, 06:26 PM
  3. Replies: 3
    Last Post: March 18th 2009, 04:19 PM

Search Tags


/mathhelpforum @mathhelpforum