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Get time from acceleration given as a function of velocity

  1. Oct 20, 2015 #1
    1. The problem statement, all variables and given/known data
    If the acceleration is given as a function of velocity a(v), we can found t(v) as t(v) = t0 + ∫vv0 1/a(v) dv.

    2. Relevant equations

    3. The attempt at a solution
    I just can't understand there to go to understand the equation..
  2. jcsd
  3. Oct 20, 2015 #2


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    Staff: Mentor

    What is the (calculus based) definition of acceleration?
  4. Oct 21, 2015 #3
    [tex]\frac{dv}{dt} = a(t) \rightarrow v(t_1) = v(t_0) + \int_{t_0}^{t_1}a(t)dt[/tex]
    [tex]\frac{dt}{dv} = \frac{1}{a(t)} \rightarrow t(v_1) = t(v_0) + \int_{v_0}^{v_1}\frac{1}{a(t)}dv[/tex]

    but it is still not [itex]a(v)[/itex]
  5. Oct 21, 2015 #4


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    Homework Helper

    How will you integrate f(t)dv? t and v are not independent variables.

    Note that acceleration a is dv/dt regardless of if a is a function of time a(t) or a function of velocity a(v)
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