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!

Physics train problem

  1. Apr 5, 2013 #1

    joshmccraney

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    A piecewise-continuous function models the velocity of a train (fps) as follows:
    $$
    v(t) =
    \begin{cases}
    80, & \text{if }\text{t>15} \\
    bt+ct^2+dt^3, & \text{if }t\text{ <15}
    \end{cases}
    $$

    How much time does it take the train to travel 5280 ft?


    2. Relevant equations
    $$(1) vdv=ads$$
    $$(2) ds=vdt$$
    $$(3) dv=adt$$

    where s is distance, v is velocity, t is time, a is acceleration


    3. The attempt at a solution
    i have: [itex]5280=80t+15^2b+15^3c+15^4d[/itex] by integrating the piecewise function and using [itex](2)[/itex]. it seems if i can find variables [itex]b,c,d[/itex] i will be done.

    i have [itex]80=bt+ct^2+dt^3[/itex] from the continuity of the function (given)

    by [itex](3)[/itex] i have [itex]0=b+2*15c+3*15^2d[/itex]

    it seems if i can find one more equation for [itex]b,c,d[/itex] i'll be done. i don't think i can use [itex](1)[/itex] as i do not have velocity as a function of distance. ive used the other two equations, so i feel i am close. any help is very appreciated. Thanks!
     
  2. jcsd
  3. Apr 5, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Your equation 5280=... looks wrong. First, 80t is not the distance travelled after the first 15 seconds. Second, check the integration itself. Third, at that point you cannot know if the 5280 ft will be reached in the first 15 second or not.

    This is not the equation you have. Where (at which time!) are the functions equal?

    Is the function piecewise-continuous (which does not help) or piecewise-continuous differentiable?
    You could add the requirement that the second derivative is the same at both sides as well, but I don't see this requirement in the problem statement.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Physics train problem
  1. Train Physics Problem (Replies: 1)

  2. Train Problem (Replies: 3)

Loading...