I know that the distance travelled in non constant acceleration is $d=\int_a^b f(x)\mathrm{d}x$, but is it possible to calculate the distance without knowing the value of $f(x)$?


closed as too localized by Waffle's Crazy Peanut, Qmechanic May 30 '13 at 13:35

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    $\begingroup$ What does $f(x)$ mean? Distance is the time integral of velocity, which is itself the time integral of acceleration. $\endgroup$ – Michael Brown May 30 '13 at 10:44
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    $\begingroup$ Please tell what is known. This is like you don't have anything and want distance covered.Think,how is it possible? $\endgroup$ – ABC May 30 '13 at 11:00
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    $\begingroup$ This question is very unclear and potentially too localized too. $\endgroup$ – Dilaton May 30 '13 at 11:20


You atleast need something known viz jerk,acceleration, velocity, displacement etc.


Analyzing the expression above, I realized that $x$ is time and $f(x)$ is a time dependent velocity. Am I right? The function $f(x)$ is not the only quantity defining the distance. This quantity as well as any other parameters of the dynamical system can be derived if you know the Hamiltonian or Lagrangian (probably with explicit time dependence in your case) and, as has been mentioned by userØØ7, initial conditions.


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