Obtain distance versus time from a speed vs distance plot.

[lostidentity]

Hi,

I have a set of experimental data given in terms of speed $u$ versus distance $x$. But I want to obtain a plot of distance $x$ versus time $t$. The problem is I don't have the end time of the experiment. In this experiment velocity is a function of distance, $u=u(x)$ and distance is in turn of time, $x=x(t)$.

$\frac{dx(t)}{dt} = u(x)$

Is this possible without knowing the start and times?

 

[gsal]

do you know the time-step of the measurements? I think that would help a lot.

Otherwise, you can probably get a couple of points from your data where the speed did not change and given the distance between points, you may be able to deduce the time-step...then, you may be able to simply have another x-axis that represent time?

 

[LCKurtz]

If you write that with the variables separated:
$$\frac {dx}{u(x)} = 1\, dt$$
couldn't you approximate the integral on the left with, for example, the trapezoidal rule using your information (x₀,u₀),(x₁,u₁),...(x_n,u_n)? But as someone else has observed, it looks like you need the times the data are recorded to put appropriate limits on the right side.