Get time from acceleration given as a function of velocity

  • Thread starter harmyder
  • Start date
  • #1
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Homework Statement


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.

Homework Equations




The Attempt at a Solution


I just can't understand there to go to understand the equation..
 

Answers and Replies

  • #2
gneill
Mentor
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What is the (calculus based) definition of acceleration?
 
  • #3
33
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[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]
 
  • #4
Nathanael
Homework Helper
1,650
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[tex]t(v_1) = t(v_0) + \int_{v_0}^{v_1}\frac{1}{a(t)}dv[/tex]
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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