- #1

rxh140630

- 60

- 11

- Homework Statement
- A particle is constrained to move along a parabola whose equation is y=x^2. At what point on the curve are the abscissa and the ordinate changing at the same rate?

- Relevant Equations
- x^2=y, dx/dy= 2x

Would the trivial solution be x=0,y=0?

Non trivial:

let [itex]y=x^2[/itex]

[itex] \frac{dy}{dx}=2x, \frac{dx}{dy} = \frac12y^{-\frac12}[/itex]

[itex]x=\frac14 y^{-\frac12}[/itex]

here x=1 and y = 1/16 is a solution

but my book says the answer is x=1/2 and y=1/4

this is one answer that you get with the equation I derived, but I feel like it's not the only answer. Am I missing something?

Non trivial:

let [itex]y=x^2[/itex]

[itex] \frac{dy}{dx}=2x, \frac{dx}{dy} = \frac12y^{-\frac12}[/itex]

[itex]x=\frac14 y^{-\frac12}[/itex]

here x=1 and y = 1/16 is a solution

but my book says the answer is x=1/2 and y=1/4

this is one answer that you get with the equation I derived, but I feel like it's not the only answer. Am I missing something?