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A powerboat, starting from rest, maintains a constant acceleration

  1. Sep 24, 2013 #1
    1. The problem statement, all variables and given/known data
    A powerboat, starting from rest, maintains a constant acceleration. After a certain time t, its displacement and velocity are r and v. At time 2t, what would be its displacement and velocity, assuming the acceleration remains the same?
    a) 2r and 2v
    b) 2r and 4v
    c) 4r and 2v
    d) 4r and 4v

    the correct answer is c

    2. Relevant equations
    v = vo + at
    x = vo + 1/2at^2


    3. The attempt at a solution
    r = vo + 1/2at^2
    r = (0) + 1/2a(2T)^2
    r = 1/2a4T^2

    v = vo + at
    v = (o) + a(2T)
    v = a2T

    i don't know what to do next because acceleration is not given so how i could i even isolate anything?
     
  2. jcsd
  3. Sep 24, 2013 #2
    What does "starting from rest" mean to you?
     
  4. Sep 24, 2013 #3
    starting from rest means initial velocity is equal to zero
     
  5. Sep 24, 2013 #4
    So you got ## v_1 = at ## and ## r_1 = at^2/2 ##. You have further found at ##2t##, ##v_2 = a(2t)## and ##r_2 = a(4t^2)/2##. All that you need to do is express ##v_2## via ##v_1## and ##r_2## via ##r_1##.
     
  6. Sep 25, 2013 #5
    what do you mean by via
     
  7. Sep 25, 2013 #6
    If you have a = 5b, and c = 10b, then you can express c via a as follows: c = 2a.
     
  8. Sep 25, 2013 #7
    Ah okay so
    if v1 = at
    and v2 = 2at
    then v2 = 2v1

    and if r1 = at^2/2
    and r2 = a4t^2/2
    r2 could be simplified into = (a2t^2)/1
    then r2 = 4r1

    right? to check,
    4r1 = 4(at^2)/2
    = 4at^2/2
    = (2at^2)/1

    which leaves me with 4v and 2v as my answer, which is c which is the correct answer :) thank you
     
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