Distance traveled in a circular motion

[Delta Sheets]

Homework Statement

A car starts from rest and accelerates around a flat curve of radius R = 31.7 m. The tangential component of the car’s acceleration remains constant at at = 2.97 m/s2, while the centripetal acceleration increases to keep the car on the curve as long as possible. The coefficient of friction between the tires and the road is μk = 0.851. What distance does the car travel around the curve before it begins to skid? (Be sure to include both the tangential and centripetal components of the acceleration.)

Homework Equations

F=(mv^2)/r
F=ma
F=μN

The Attempt at a Solution

mv^2/r=μN
mv^2/r=μmg
μg=v^2/r
v^2=rμg
v^2=v(initial)^2+2ax
rμg=2ax
x=rμg/(2a)
x=(31.7)(.851)(9.81)/(2(9.81))
x=44.55m
This is how i attempted the problem, but am apparently incorrect. What am i doing wrong?

 

[ehild]

The static friction that acts at the tyres has to cover the total accelerating force which includes both centripetal and tangential acceleration.

ehild