Parametric Equation Speed


by keemosabi
Tags: equation, parametric, speed
keemosabi
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#1
Feb12-09, 10:09 PM
P: 109
1. The problem statement, all variables and given/known data
Can someone please tell me how to get the average speed of a particle moving along a path represented by parametric equations? Is it [latex]\frac{1}{b-a}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2}[/latex]

Isn't this the arc length formula?
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w3390
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#2
Feb12-09, 10:13 PM
P: 344
This is the arc length formula. The average value formula is Favg=(1/b-a)INT[f(x)dx]. It seems you combined two formulas.
keemosabi
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#3
Feb12-09, 10:38 PM
P: 109
Quote Quote by w3390 View Post
This is the arc length formula. The average value formula is Favg=(1/b-a)INT[f(x)dx]. It seems you combined two formulas.
But if I wanted the speed of a particle moving with a parametric graph, woldn't everything under the radical be my speed function?

w3390
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#4
Feb12-09, 10:40 PM
P: 344

Parametric Equation Speed


Actually, you may be right. I think that might actually work.
Dick
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#5
Feb13-09, 12:27 AM
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No, no, no. The average speed is displacement over time. It has nothing to do with arc length. It's sqrt((x(b)-x(a))^2+(y(b)-y(a))^2)/(b-a) where a is the intiial time and b is the final time. Right?
keemosabi
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#6
Feb13-09, 08:11 AM
P: 109
Quote Quote by Dick View Post
No, no, no. The average speed is displacement over time. It has nothing to do with arc length. It's sqrt((x(b)-x(a))^2+(y(b)-y(a))^2)/(b-a) where a is the intiial time and b is the final time. Right?
Couldn't you also do the average value of the absolute value of the velocity graph?
Dick
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#7
Feb13-09, 08:53 AM
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Quote Quote by keemosabi View Post
Couldn't you also do the average value of the absolute value of the velocity graph?
Yes, you could. In which case that would be correct. Distance travelled/time could also be considered an average speed. I was only thinking of the displacement/time definition.
keemosabi
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#8
Feb13-09, 10:02 AM
P: 109
Quote Quote by Dick View Post
Yes, you could. In which case that would be correct. Distance travelled/time could also be considered an average speed. I was only thinking of the displacement/time definition.
Alirght, thank you for the help.

Also, is there any way to determine if a particle traveling on a parametric path is increasing in speed? I know I can determine if the x and y are accelerating, but I can I determine if the particle itself is increasing?

What if it was accelearating in the x direction but decelerating in the y? Would the particle's speed be increasing or decreasing?
Dick
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#9
Feb13-09, 10:11 AM
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The 'speed' is sqrt((dx/dt)^2+(dy/dt)^2), isn't it? Just look at whether that quantity is increasing or decreasing.


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