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Determine an expression for distance traveled and the time elapsed

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data

    A self propelled vehicle of mass m travels in a straight line. The vehicle has an engine which provides constant power P so that the acceleration 'a' at an instant is given by a=P/mv where v is the speed of the vehicle and all frictional resistance is neglected. Determine expressions for:

    a) the distance traveled,

    b) the time elapsed


    2. Relevant equations

    a=P/mv


    3. The attempt at a solution

    I took the derivative of a so,

    a=dv/dt then tried to get to v=ds/dt

    I ended up with this

    ds/dt=sqrt(2p/m + Vo^2)
     
  2. jcsd
  3. Jan 21, 2012 #2

    tiny-tim

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    welcome to pf!

    hi thestiggg! welcome to pf! :smile:
    you mean ds/dt=√(2pt/m + vo2) ? :wink:

    but i suspect the question wants answers to a) and b) as functions of v …

    try the standard chain rule trick a = dv/dt = dv/ds ds/dt = v dv/ds :smile:
     
  4. Jan 21, 2012 #3
    Yes sorry I missed the t but that's what I meant. I'll give it a try and get back to you

    EDIT: and should I integrate and evaluate to v, vo, s and so?
     
  5. Jan 21, 2012 #4

    tiny-tim

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  6. Jan 21, 2012 #5
    Is it safe to assume that vo, so is = 0 according to the question?
     
  7. Jan 21, 2012 #6
    Okay so for a) I used "v dv = a ds " and I got " (m/p)*((v2^3-v1^3)/3) + so = s "

    For b) I used a=dv/dt and I got " t= (m/p)*((v2^2-v1^2)/2) "

    Does that look reasonable?
     
  8. Jan 21, 2012 #7

    tiny-tim

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    i don't think so
     
  9. Jan 22, 2012 #8

    tiny-tim

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    oops!

    oh i'm sorry! :redface:

    i was replying to your post #5, i didn't notice your post #6 at all (it came in a few seconds before mine) …
    yes, that's fine! :smile:

    (except for the constants in the first one: you need either a constant s0 or a constant v0, not both!

    also, you should use v and v0, not v1 and v2 :wink:)
     
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