# Obtain distance versus time from a speed vs distance plot.

• lostidentity
In summary, the conversation discusses how to obtain a plot of distance versus time using experimental data given in terms of speed versus distance. It is suggested to use the time-step of the measurements or approximate the integral using the trapezoidal rule to determine the necessary time information.
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?

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?

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.

## 1. What is the purpose of obtaining distance versus time from a speed vs distance plot?

The purpose of obtaining distance versus time from a speed vs distance plot is to determine the relationship between distance and time for a given object's motion. This can help in analyzing the speed and acceleration of the object, as well as predicting its future position at any given time.

## 2. How do you obtain distance versus time from a speed vs distance plot?

To obtain distance versus time from a speed vs distance plot, you can use the slope of the line on the graph. The slope represents the speed of the object, and the distance can be calculated by multiplying the speed by the time interval between each data point. This will give you a set of data points that can then be plotted on a distance versus time graph.

## 3. What is the difference between speed and distance on a plot?

Speed and distance are two different measures of an object's motion. Speed is the rate at which an object is moving, while distance is the total amount of ground covered by the object. On a plot, speed is represented by the slope of the line, while distance is represented by the data points on the y-axis.

## 4. What can a speed vs distance plot tell us about an object's motion?

A speed vs distance plot can tell us about an object's motion by showing us how its speed changes over time. The slope of the line can give us information about the object's acceleration, and the overall shape of the plot can indicate if the object is moving at a constant speed or changing its speed over time.

## 5. How can we use the information from a speed vs distance plot in real-world applications?

The information from a speed vs distance plot can be used in various real-world applications, such as in analyzing the motion of vehicles, predicting the travel time for a trip, or understanding the performance of athletes in sports. It can also help in designing and optimizing transportation systems, such as highways and railways, for more efficient and safer travel.

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