A car starts from rest with a constant tangential acceleration `a_(0)` in a circular path of radius r. At time t, the car kids, find the value of coefficient of friction.

Explanation

The tangential and centripetal acceleration is provided only by the frictionless force.
`Thus, f sin theta, fcos theta=(mv^(2))/(r)=(m(a_(0)t)^(2))/(r)`
`Rightarrow f=m sqrt(a_(0)^(2)+((a_(o)t)^(4))/(r^(2)))=ma_(0)sqrt(1+a_(0)^(2)t^(4))/(r_(2))=f_("max")`
`mumg=ma_(0) sqrt(1+(a_(0)^(2)t^(4))/(r^(2))) Rightarrow mu=(a_(0))/(g)sqrt(1+(a_(0)^(2)t^(2))/(r^(2)))`