A car travels in a circular road having angular velocity defined as q = t+t2+t3, where r = 10 m. Find the radial and transverse components of the velocity of the car after 10 sec.

1) 3210, 0
2) 5400, 0
3) 0, 4600
4) 6, 4500

The angle is defined by the relation q = t+t2+t3, differentiating with respect to time, angular velocity
dq/dt  = 1+2t+3t2, and at t = 10 sec
dq/dt  = 1+2(10)+3(10)2 = 321 rad/sec

Since the car is travelling in a circular path the length of the path at an angle q is given by s = rq, differentiating the equation with respect to time, we get
vq = ds/dt = r dq/dt, dq/dt = 321 rad/sec
radial velocity vq = 10(321) = 3210 m/sec
transverse velocity vt = 0, velocity v = vq = 3210m/sec

Radial velocity component vq = 3210 m/sec Transverse velocity component vt = 0 m/sec

So, the radial and transverse velocity components are 3210 m/sec and 0 m/sec.