Question

A car moves with constant tangential acceleration aT = 0.80 m/s 2 along a horizontal surface circumscribing a circle of radius R = 40 m. The co-efficient of sliding friction between the wheels of the car and the surface is = 0.20. What distance will the car move without sliding if its initial velocity is zero ?

Answer 1

u = 0
v = velocity of the car at  t sec.  =  u + a_t * t = 0.80 t      m/s

friction force supplies the centripetal acceleration/force.  If friction is not able to supply that, then the car cannot circumscribe a circular path.

Friction = μ m g

        μ g >= Radial acceleration = a_r 
        μ  g >=  v² / R

        0.2 * 10 >= 0.64 t² /40
 
         t <= 5 √5 sec.  

distance traveled = 1/2 * 0.8 * t² = 50 m

Answer 2

Since centrifugal force is supported by friction ,for body to continue moving in a circular path

Therefore ,

Coefficient of friction × mg = mv^r/r

V^2= coefficient of friction×r×g. (Mass gets cancelled)

V^2=80

V=4√5 m/s

V^2 -u^2 = 2as

V^2= 2as. (U=0)

S= (4√5)^2/2a

S= 16×5×/2×0.8

S=50 m