Results 1 to 3 of 3

Math Help - Particle movement through space #2

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    39

    Particle movement through space #2

    A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

    Find the velocity at time t.
    What is the velocity after 3 s?
    When is the particle at rest?
    When is the particle moving in the positive direction?
    Find the total distance traveled during the first 8 seconds.
    Find the acceleration at time t after 3 s.
    When is the particle speeding up? When is it slowing down?

    The equation is: f(t) = te^(-t/2)

    I don't quite understand how do to this problem so a complete explanation would be best.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Neversh View Post
    A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

    Find the velocity at time t.
    What is the velocity after 3 s?
    When is the particle at rest?
    When is the particle moving in the positive direction?
    Find the total distance traveled during the first 8 seconds.
    Find the acceleration at time t after 3 s.
    When is the particle speeding up? When is it slowing down?

    The equation is: f(t) = te^(-t/2)

    I don't quite understand how do to this problem so a complete explanation would be best.
    The velocity is:

    v(t)=\frac{ds}{dt}=\frac{d}{dt} \left(t e^{-t/2} \right)

    which should allow you to answer the first two questions.

    The third question is asking at what time is v(t)=0

    The fourth is asking when is v(t)>0

    I will skip over the fifth

    For the sixth you need to know that acceleration:

    a(t)=\frac{d}{dt}v(t)

    The last is asking when is a(t)>0

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Neversh View Post
    A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

    Find the velocity at time t.
    What is the velocity after 3 s?
    When is the particle at rest?
    When is the particle moving in the positive direction?
    Find the total distance traveled during the first 8 seconds.
    Find the acceleration at time t after 3 s.
    When is the particle speeding up? When is it slowing down?

    The equation is: f(t) = te^(-t/2)

    I don't quite understand how do to this problem so a complete explanation would be best.
    For #5, draw a graph of s versus t over the interval t = 0 to t = 8. You will need to calculate the s-coordinate of the turning point (use your answer to #3, which I will denote by t = \alpha). The distance travelled should then be easily seen to be [s(\alpha) - s(0)] + [s(\alpha) - s(8)] = ....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Particle movement through space.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 19th 2010, 05:08 PM
  2. Particle Movement through space #3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2010, 10:38 PM
  3. stochastic particle movement probabilities
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 9th 2010, 02:55 PM
  4. Opposite Movement in a 2D Space...
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: September 9th 2009, 06:19 PM
  5. particle movement
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 12th 2009, 02:53 PM

Search Tags


/mathhelpforum @mathhelpforum