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A Hard kinematic problem

  1. Mar 24, 2007 #1
    1. The problem statement, all variables and given/known data

    if you knew that the acceleration of a body is inversely proportional with square the time from the time interval (t=2'' to t=10''), and at t=2'' its velocity was V=-15 m/sec., and at t=10'' its velocity was V=-0.36 m/sec. if its postion from the origin point at t=2'' is twice as much at t=10'', find

    1-the position of the body at t=2'' and at t=10''
    2-the distance covered from the time interval (t=2'' to t=10'')

    2. Relevant equations

    a=v(dv/dx) or dv/dt........v=dx/dt........D=r-r'..........r is the position vector

    3. The attempt at a solution

    i put the relation in the form


    i got the relation that a2=25a10

    then i integrated to get that

    integration (dv2/dt)=25 integration (dv10/dt)


    then i used the velocities were given to me to get


    then i couldn't go on, because i don't know what i am getting and what for

    can you help me please?
  2. jcsd
  3. Mar 24, 2007 #2


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    Science Advisor
    Homework Helper

    Your basic given equation is a(t)=dv(t)/dt=A/t^2 for some A. So integrate that to get expressions for v(t) and x(t) being sure to keep constants of integration. You'll get two of them. So now you have three unknown constants and three 'boundary conditions'. So you should be able to solve for all of the constants and answer any questions you need to.
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