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Time-dependent force

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data

    A time-dependent force, F = (8.00i – 4.00tj) N, where t is in seconds, is exerted on a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s? (b) How far is the object from its initial position when its speed is 15.0 m/s? (c) Through what total displacement has the object traveled at this moment?


    2. Relevant equations

    F = ma
    a = d/t

    3. The attempt at a solution

    (a)
    F = ma

    (8.00i – 4.00tj) N = (2.00 kg)(15.0 m/s)

    t = 2s


    (b)
    a = d/t

    (15.0 m/s2)(t) = d

    I don't see why it's not 2 seconds. Is it not just algebra, did I leave out a significant part of the equation? Thanks, this site has taught me quite a bit.
     
  2. jcsd
  3. Sep 23, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    F = ma = (8i - 4jt) N. m is given. So
    a = 4i - 2jt. You can write a = dv/dt. So
    dv = 4i*dt - 2jt*dt.
    Take integration with respect to time.
    v = 4i*t - jt^2 + C. When t = 0 , vo = 0. So C = 0.
    The magnitude of v is given
    And v^2 = (4t)^2 + t^4
    Put the value of v and solve for t.
     
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