
A car travels in a
circular road having angular velocity defined as q
= t+t^{2}+t^{3}, 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+t^{2}+t^{3}, differentiating with respect
to time, angular velocity
dq/dt =
1+2t+3t^{2}, 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
v_{q}
= ds/dt = r dq/dt,
dq/dt
= 321 rad/sec
radial velocity v_{q} =
10(321) = 3210 m/sec
transverse velocity
v_{t} = 0, velocity v = v_{q}
= 3210m/sec
Radial velocity component v_{q}
= 3210 m/sec Transverse velocity component v_{t} = 0 m/sec
So, the radial and transverse velocity components are 3210 m/sec and
0 m/sec.
