(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A body is moving on a trajectory [tex] \frac{x^2}{a^2} + \frac{y^2}{b^2} =1 [/tex] vith a constant speed [tex] v_{0} [/tex]. Find its velocity [tex] \vec{v} [/tex] and acceleration [tex] \vec{a} [/tex].

2. Relevant equations

As far as I know [tex] \vec{a} = \vec{a}_{\tau} + \vec{a}_{n} = \frac{dv}{dx}\vec{\tau} + \frac{d\vec{\tau}}{dx}v [/tex]

3. The attempt at a solution

Since v=const, [tex] \frac{dv}{dx}\vec{\tau} = 0 [/tex] and therefore [tex] \vec{a} = 0 + \frac{d\vec{\tau}}{dx}v = \frac{v^{2}_{0}}{\rho}\vec{n} [/tex] where [tex] \rho [/tex] is the radius. Since we are dealing with an ellipse, the radius is a function of x and y, but I don't know how to express [tex] \rho [/tex] as [tex] \rho(x,y) [/tex]

I think that I can express velocity and acceleration like this:

[tex] \vec{v}=v_{0}(\frac{y}{b} , \frac{x}{a}) [/tex]

[tex] \vec{a}=\frac{v^{2}_{0}}{\rho}(\frac{x}{a} , -\frac{y}{b}) [/tex]

If so far everything has been correct (although I doubt about it) the only problem is expressing the radius [tex] \rho(x,y) [/tex].

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# Homework Help: Body moving on an ellipse; find velocity, acceleration

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