# 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?

Homework Helper
Gold Member
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),...(xn,un)? 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.