Circular motion with tangential acceleration

[vu10758]

A car is initially at rest. It starts mvoing with tangential acceleration a_tan along a flat circular track of radius r. If the coefficient of static friction is mu, determine the total distance traveled by the car before it skids off the track.

This is what I did.

I drew the free body diagram with normal force point up, mg pointing down, and f point right, and acceleration (not on the diagram) is pointing left towards the center. Is this the correct diagram?

I know N=mg

and

F = ma
F = m (v^2)/r

so v=SQRT(Fr/m)

I know d = (1/2)at^2

Where do I go from here to find the distance. I don't have acceleration and time.

[physics girl phd]

In your free body diagram, you are missing something that relates to the friction...

[aster]

Just think about which is the force that keeps the car in circular motion.
(The answer is d = mu*g*r/2a.)

[Doc Al]

Just think about which is the force that keeps the car in circular motion.
(The answer is d = mu*g*r/2a.)
Please DO NOT provide answers--instead, help the poster do their own work.

In any case, that answer is incorrect. Hint: Static friction must provide the total acceleration.