A car starts from rest on a flat circular track of radius $50\ \text{m}$. It speeds up along the track with a steady tangential acceleration of $3.0\ \text{m/s}^2$. The coefficient of static friction between the tyres and the road is $0.50$. Take $g = 10\ \text{m/s}^2$. How far along the track does the car go before its tyres begin to skid?