Circular Motion: Tangential and Normal Acceleration

[Heexit]

Homework Statement

A particle moves in a circular path of radius R in such a way that the tangential acceleration is equal to the normal acceleration. Determine the velocity as a function of time t and the initial velocity (v_0).

Relevant Equations

N/A

Hello Physicsforum!

This is my attempt:
First I realised:
$a_s=a_n$

Secondly I used since previus known formulas:
$a_n=\frac {v^2} {R}$
$v=v_0+a_s*t$

Although now I do not know how to continue, any suggestions would be appriciated!
Thanks for your help on beforehand

 

[haruspex]

$v=v_0+a_s*t$

That is only if the tangential acceleration has constant magnitude.
What equation relates $a_s$ to $v_s$ more generally?

Unless you have left out some information, there is no way to determine $v_0$.

 

[Heexit]

That is only if the tangential acceleration has constant magnitude.
What equation relates $a_s$ to $v_s$ more generally?

Unless you have left out some information, there is no way to determine $v_0$.

Thanks for your help!

The only equation that I can think of is:
$a_s=\frac {dv} {dt}$
Anything more than that I can't think of :/

There might have been some inaccurate translation on my side, sorry about that. The question does not ask us for a define value of $v_0$, rather an expression of variables, see solution in picture below:

 

[haruspex]

The only equation that I can think of is:
$a_s=\frac {dv} {dt}$

That will do nicely. Combine that with your other information.

The question does not ask us for a define value of $v_0$, rather an expression of variables, see solution in picture below:
View attachment 327036

Ok.

 

[Heexit]

Thanks for your help!
Here is my solution:

 

[haruspex]

Thanks for your help!
Here is my solution:
View attachment 327037

Good.