Flat Curve with Friction (Unbanked Road)

Questions about an object (car, cyclist, coin) moving on a flat horizontal circular path where friction provides the centripetal force, asking for maximum speed, minimum radius, or slipping conditions.

jee-main 2002 Q6 View
The minimum velocity (in $\mathrm{ms}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is
(1) 60
(2) 30
(3) 15
(4) 25
jee-main 2005 Q14 View
Consider a car moving on a straight road with a speed of $100 \mathrm{~m}/\mathrm{s}$. The distance at which car can be stopped is $[\mu_\mathrm{k} = 0.5]$
(1) 800 m
(2) 1000 m
(3) 100 m
(4) 400 m
jee-main 2022 Q22 View
A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be $30 \mathrm{~m~s}^{-1}$ without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be $\_\_\_\_$ $\mathrm{m~s}^{-1}$.