$A$ car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$,the minimum radius of the arc in meters in which the car turns is:

The maximum speed of a car on a road turn of radius $30\,m$; if the coefficient of friction between the tyres and the road is $0.4$; will be ........ $m/s$. (in $.84$)

$A$ child starts running from rest along a circular track of radius $r$ with constant tangential acceleration $a$. After time $t$,the child feels that the shoes have started slipping on the ground. What is the coefficient of friction $\mu$ between the shoes and the ground? $[g = \text{acceleration due to gravity}]$

$A$ curve on a level road has a radius of $75 \, m$. The maximum speed of a car turning this curved road can be $30 \, m/s$ without skidding. If the radius of the curved road is changed to $48 \, m$ and the coefficient of friction between the tyres and the road remains the same,then the maximum allowed speed would be ......... $m/s$.

For a banked curved road,if the velocity of the vehicle $v < v_0$ (where $v_0$ is the optimum speed),what is the direction of the frictional force?

Write the formula for the maximum safe speed of a vehicle moving on a flat curved road of radius $r$.