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Acceleration, velocity, displacement & time

  1. Aug 26, 2014 #1
    1. The problem statement, all variables and given/known data
    a = 2/(0.1v+1)
    At t = 0; s = 0, v = 0

    1) Derive a relationship between t and v
    2) Derive a relationship between displacement (s) and v
    3) Draw v vs t for 0s ≤ t ≤ 75s & s vs t for 0s ≤ t ≤ 50s graphs

    2. Relevant equations
    a = dv / dt
    v = ds / dt


    3. The attempt at a solution
    For part (1) find the integral of dv = a.dt

    For part (2) find the integral of ds = v.dt

    For part (3) graph the equations found from the integrations above and graph a suitable scale.

    Where I'm stuck;
    1) Not really sure I've got the terms the correct way in part 2.
    2) when integrating dt, what happens to this term? Does it become 0, 1 or t?

    (I'm not looking for the answer, but to check my approach and also find out what happens to the dt term as this is the first course I've seen dt / d? terms rearranged.)

    Thanks
     
  2. jcsd
  3. Aug 26, 2014 #2
    Show us how you solved part 1, and what your result was. Have you had differential equations yet?

    Chet
     
  4. Aug 26, 2014 #3

    SteamKing

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    Science Advisor
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    What usually happens when you integrate d(something)?

    ∫dx = ?

    ∫dt = ?

    Isn't dt the same as 1[itex]\cdot[/itex]dt?

    You should take a quick integration review.
     
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