A cyclist starts from rest and accelerates at the rate of 0.25 m/s2 for 10 s on a straight road. At time t = 10 s, the cyclist enters a circular track and cycles with uniform velocity. He completes one round of the track in 50 s. what is the radius of track ?

A cyclist starts from rest and accelerates at the rate of 0.25 m/s2 f

1.	A cyclist starts from rest and accelerates at the rate of 0.25 m/s2 for 10 s on a straight road. At time t = 10 s, the cyclist enters a circular track and cycles with uniform velocity. He completes one round of the track in 50 s. what is the radius of track ?
Answer» AnswerNet acceleration is due to braking and centripetal accelerationDue to Braking,a T =0.5m/s 2 Speed of the cyclist, v=27km/h=7.5m/sRadius of the CIRCULAR turn, r=80mCentripetal acceleration is GIVEN as:a c = rV 2 =(7.5 2 )/80=0.70m/s 2 Since the angle between a c and a T is 900, the resultant acceleration a is given by:a=(a C2 +a T2 ) 1/2 a=(0.7 2 +0.5 2 ) 1/2 =0.86m/s 2 tanθ= a T a c where θ is the angle of the resultant with the direction of the velocity. tanθ= 0.50.7 =1.4θ=tan −1 (1.4)=54.