What is the maximum velocity of a motorbike on a curved track?

[Saitama]

At $v_{max}$ what is the direction of the total acceleration?

Towards the center? So $v_{max}=\sqrt{\mu gR}$?

 

[TSny]

Towards the center? So $v_{max}=\sqrt{\mu gR}$?

Yes.

 

[Saitama]

Yes.

Thank you TSny!

Substituting this value of $v_{max}$ in the final equation, I get $s_{min}=\pi R/4$.

 

[TSny]

I get $s_{min}=\pi R/4$.

I think that's right.