A insect starts crawling towards the center with a constant velocity of 0.5 m / s just when the disc starts rotating with an angular velocity of 2 t rad /s. Here t is the time in seconds. The radius of the disc is 1 m. Determine the  magnitude  of  the  insect's velocity at t = 1 s.

a) 1.00 m / s
b) - 0.50 m / s
c) 1.19 m / s
d) 0.92 m / s

Radial velocity of the insect v _r = - 0.5 m / s .
Angular velocity at t = 1 s is 2 ( 1 ) = 2 rad / s .

The radial distance covered by the insect till the instant t = 1 s is given by,

At t = 1 s the insect is situated at 1 - 0.5 = 0.5 m from the center.

Hence the radial ( v _r ) and the transverse component of the velocity ( v _q ) are given by,

The magnitude of the insect's velocity is,

The magnitude of insect 's velocity at t = 1 second is 1.19 m / s .