
#1
Feb1209, 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}{ba}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2}[/latex] Isn't this the arc length formula? 



#2
Feb1209, 10:13 PM

P: 344

This is the arc length formula. The average value formula is Favg=(1/ba)INT[f(x)dx]. It seems you combined two formulas.




#3
Feb1209, 10:38 PM

P: 109





#4
Feb1209, 10:40 PM

P: 344

Parametric Equation Speed
Actually, you may be right. I think that might actually work.




#5
Feb1309, 12:27 AM

Sci Advisor
HW Helper
Thanks
P: 25,165

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)/(ba) where a is the intiial time and b is the final time. Right?




#6
Feb1309, 08:11 AM

P: 109





#7
Feb1309, 08:53 AM

Sci Advisor
HW Helper
Thanks
P: 25,165





#8
Feb1309, 10:02 AM

P: 109

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? 



#9
Feb1309, 10:11 AM

Sci Advisor
HW Helper
Thanks
P: 25,165

The 'speed' is sqrt((dx/dt)^2+(dy/dt)^2), isn't it? Just look at whether that quantity is increasing or decreasing.



Register to reply 
Related Discussions  
parametric equation  Calculus & Beyond Homework  2  
Parametric Equation  Calculus & Beyond Homework  1  
Parametric equation  Calculus & Beyond Homework  5  
Parametric equation  Advanced Physics Homework  5  
parametric equation  Calculus  8 