# Parametric Equation Speed

by keemosabi
Tags: equation, parametric, speed
 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 $\frac{1}{b-a}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2}$ Isn't this the arc length formula?
 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.
P: 109
 Quote by w3390 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?

P: 344

## Parametric Equation Speed

Actually, you may be right. I think that might actually work.
 HW Helper Sci Advisor Thanks P: 24,422 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?
P: 109
 Quote by Dick 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?
HW Helper
Thanks
P: 24,422
 Quote by keemosabi 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.
P: 109
 Quote by Dick 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?
 HW Helper Sci Advisor Thanks P: 24,422 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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