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When acceleration depends on the distance

  1. yes

    1 vote(s)
    100.0%
  2. no

    0 vote(s)
    0.0%
  1. Jan 25, 2013 #1
    1. The problem statement, all variables and given/known data
    i am trying to find out velocity at a point of time and distance covered by a particle whose acceleration (a) depends on distance (s). to start with let a = k*s+c were k and c are contants.


    2. Relevant equations
    a= k*s+c
    we know a=ds/st


    3. The attempt at a solution
    a=k*s+c

    (dv/dt)=k*s+c
    or
    v=k*s*t+s*t

    but i know (s) is not to be treated as conatant... then what to do here?? please help
    i cannot frame the differential equation
     
  2. jcsd
  3. Jan 25, 2013 #2
    a = dv/dt = dv/ds ds/dt = dv/ds v
     
  4. Jan 25, 2013 #3

    Dick

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    Science Advisor
    Homework Helper

    a(t)=v'(t)=s''(t). So s''(t)=k*s(t)+c. It's a second order ode. Like a harmonic oscillator.
     
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