# How find distance of total covered by moving Point?

Math123 shared this question 2 years ago

How to find a distance covered by moving point? Length( ) command is also useful to measure lengths on functions or curves. 2

if you move a point freely, you can't. If you move a point on a segment, you could mark the starting point and define a segment between this starting point and the position of the the moving point. Then the length of this segment is shown on the Algebra View. For a point moving on a function, you have the known integral formulas.

chris 1

i tried integral Length formula but it doesn't work. and also it subtract the negative area, Can you pls share the formula and calculation. It will be very useful because it increase the length as point moving and cannot subtract and negative area of function.  2

Length( ) command is also useful to measure lengths on functions or curves. 1

Thanks  3

Hi,

approximative distance covered by moving free point.

... 1

Dear @Patrick I tried to make distance approximation as you attached , but it did not work. Like Point M (On Update) script as well as List P is not updating . Pls share the step by step process. 1

you can learn how Patrick did it in the definitions in Algebra View of his file. Select the option to show the definition of the objects in the View instead of their values. And if you sort them in the order they were created you 've got it all

chris 1

Yes i have tried this in many ways by looking definition and script . i am not able to make this in my project. 1

So then, what is your project ?... 1

I make parametric function which represent the motion of particle with slider parameter slider 't' so that it motion restricted within domain not in the whole function. I want to distance covered by particle. From minimum value slider which can be picked automatically as initial condition . also as particle move also distance calculated.

I want two things min value from slider as i change the f(min) and second distance as slider moves. Integral command is not working it subtract the negative area. Length command give me total distance within range not as slider moves, 1

Pls see attaached  2

```Integral command is not working it subtract the negative area.
```

Please post your file with the Integral() command. Maybe you can use NIntegral(abs(... rather than Integral(... 1

Pls see attached. Nintegral is alo not working here. 1

Thanks it worked with absolute value. 1

But it Nintegral does not give me accurate result (rather less distance) and Length function gives me accurate results.

Nintegral(abs(t),0,t) = 28.46

Integtegral(abs(t),0,t} = 50

Length(f,0,t) = 37.68 (accurate)

Why all three has three different results of same function. f(t) has negative area in some region. 