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M2 help - again

Discussion in 'Mathematics' started by Maths_Mike, Aug 14, 2011.

  1. Maths_Mike

    Maths_Mike New commenter

    Ok - i know i need to differentiate to get the velocity and then set it to 0 - but I cant seen to get it to work.
    s=1/k(g/k +U)(1-e^-kt)-gt/k where k and U are constants. Model valid while particle moving upwards.
    Show valid while 0<=t<= 1/k ln(1+kU/g)
     
  2. Maths_Mike

    Maths_Mike New commenter

    Ok - i know i need to differentiate to get the velocity and then set it to 0 - but I cant seen to get it to work.
    s=1/k(g/k +U)(1-e^-kt)-gt/k where k and U are constants. Model valid while particle moving upwards.
    Show valid while 0<=t<= 1/k ln(1+kU/g)
     
  3. DM

    DM New commenter

    Can you put some brackets in to make it clear which bits are on the top or bottom of the fraction?
     
  4. Maths_Mike

    Maths_Mike New commenter

    (1/k)(g/k +U)(1-e^-kt)-(gt/k)
    (1/k)ln(1+kU/g)
     
  5. DM

    DM New commenter

    Your method works. What did you get for v?
     
  6. DM

    DM New commenter

    Got fed up pressing refresh.
    You should have obtained:
    v = exp(-kt) ((g/k) + U) - (g/k)
     
  7. Maths_Mike

    Maths_Mike New commenter

    crumbs sry for the not very quick reply!
     
  8. DM

    DM New commenter

    Is that what you had?
     
  9. Maths_Mike

    Maths_Mike New commenter

    anyway it seems i made a mistake with my differentiating!
     
  10. DM

    DM New commenter

    Ok.
     
  11. Maths_Mike

    Maths_Mike New commenter

    on hang on - i just didnt cancel the 1/k with the (ke^-kt)
    [​IMG]
     
  12. Maths_Mike

    Maths_Mike New commenter

    may still need some more help!
     
  13. DM

    DM New commenter

    On this or something else?
     
  14. Maths_Mike

    Maths_Mike New commenter

    this.
    i have got e^-kt = (gk/g+kU)
    but still stuck!
     
  15. DM

    DM New commenter

    You should have e^(-kt) = g/(g + kU) so an extra k has crept in.
     
  16. Maths_Mike

    Maths_Mike New commenter

    just got it! thanks again!
     
  17. DM

    DM New commenter

    I did:

    g/k = (g/k + U) exp(-kt)

    g/k = ((g + kU)/k) exp(-kt)

    exp(kt) = (g + kU)/g

     
  18. Maths_Mike

    Maths_Mike New commenter

    I am ok to say that if e^-kt = 1+(g/kU) then e^kt = 1+(kU/g) -- i.e sort of doing the reciprocal of both sides - or is there a better way of explaining this?
     
  19. Maths_Mike

    Maths_Mike New commenter

    Ok just got your last post so all clear - thanks
     
  20. DM

    DM New commenter

    That looks like you are saying if x = a + b then 1/x = 1/a + 1/b.
     

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