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patbatE21

Calculus II: Starting at s = 0 when t = 0, an object moves along a line so that its velocity at time t is v(t) = 2t - 4 centimeters per second. How long will it take to get to s = 12? To travel a total distance of 12 centimeters?

  • 2 years ago
  • 2 years ago

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  1. patbatE21
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    I have t=6

    • 2 years ago
  2. ktklown
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    hold on, i'll compute and see if it matches

    • 2 years ago
  3. patbatE21
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    v(t) = 2t - 4 s(t) = integral 2t - 4 = 2t^2 - 4t + C 0 = 0^2 -4(0) + C t^2 - 4t = 12 t^2 -4t -12=0 (t-6)(t-2) t= 6 considering time is never negative

    • 2 years ago
  4. patbatE21
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    Grrrrrrr Idk HHHHEEEEELLLLLPPPPPP

    • 2 years ago
  5. Arnab09
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    that will be (t-6)(t+2)

    • 2 years ago
  6. ktklown
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    yes i get 6 also

    • 2 years ago
  7. Arnab09
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    second thing, u have made the displacement 0, but actually distance is needed

    • 2 years ago
  8. patbatE21
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    he is correct

    • 2 years ago
  9. Arnab09
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    sorry, u have made displacement 12 :)

    • 2 years ago
  10. ktklown
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    yes since the velocity starts out negative, the object is going backwards at first, then goes forwards. do you want the total displacement to be 12 or the position from the starting point to be 12?

    • 2 years ago
  11. patbatE21
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    Arnab09 would that mean I would have to integrate as such|dw:1321863723148:dw|

    • 2 years ago
  12. Arnab09
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    total distance covered, i guess

    • 2 years ago
  13. ktklown
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    if you want the total displacement to be 12, then you first solve to find out where the object stopped (0 velocity) by setting v(t)=0. then plug in that t value to s(t).

    • 2 years ago
  14. patbatE21
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    Ktklown the total distance

    • 2 years ago
  15. ktklown
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    OK, so first solve to see where the object changed direction. that happened when v(t)==0, i.e. at t=2

    • 2 years ago
  16. patbatE21
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    ok

    • 2 years ago
  17. ktklown
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    at t=2 the object was at -4. then it starts going forward, so its total displacement will equal 12 when it reaches +4

    • 2 years ago
  18. ktklown
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    i.e. from start (0) to -4, then from -4 back to 0 for a total of 8, then from 0 to +4 for a total of 12

    • 2 years ago
  19. patbatE21
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    ok

    • 2 years ago
  20. ktklown
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    it looks like that happens at 2+2sqrt(3) =t

    • 2 years ago
  21. Arnab09
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    yeah,@ ktklown, u r right :)

    • 2 years ago
  22. Arnab09
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    put the position 8 inspite of 12, u will get the answer

    • 2 years ago
  23. ktklown
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    It looks like, from reading the original question, they want to know both answers. First when does it reach s=12, and second when does it travel a total of 12 (in which case we do the other computation we just finished)

    • 2 years ago
  24. Arnab09
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    in the question, the term is 'distance', not 'displacement' so the second method is correct, definitely..

    • 2 years ago
  25. patbatE21
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    I've worked it out 4 times today, I'm probably just bad at this

    • 2 years ago
  26. ktklown
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    well it specifically says "s=12", so it seems to me like they are asking both versions. i don't know, it's not very clearly worded

    • 2 years ago
  27. Arnab09
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    maybe, if s (displacement) =12, then t^2-4t=12 and t=6

    • 2 years ago
  28. ktklown
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    yeah, if i were doing this as homework i'd probably write the answer for both interpretations

    • 2 years ago
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