Deriving radial and tangential acceleration in polar coordinates

[dirk_mec1]

Homework Statement

Homework Equations

Formulas for a_r and a_theta.

The Attempt at a Solution

I got the second derative of r but I think the fluxie v is a mistake. I am sure that
$\dot{v} =a\$, right?

 

[haruspex]

The statement of the question is rather unclear. If v is the velocity, dv/dt is a vector, but it doesn't ask about the direction. Maybe it means to ask for $|\dot{\vec v}|$.
The given acceleration appears to be the radial component only, so is not the same as either $|\dot{\vec v}|$ (the total acceleration) or $\ddot r$.

 

[dirk_mec1]

Yes but the radial acceleration is the total acceleration $a =a _r$ so it should be the same right?