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.